#install.packages("modelsummary")
#install.packages("ggplot2")
#install.packages("dplyr")
#install.packages("haven")
#install.packages("tidyverse")
#install.packages("tidyr")
#install.packages("kernlab")
#install.packages("randomForest")
#install.packages("glmnet")
#install.packages("tidymodels")
#install.packages("dotwhisker")
#install.packages("vip")
#install.packages("Rtsne")
#install.packages("cowplot")
#install.packages("ggdendro")Predicting the occurrence of steatosis and cirrhosis based on transient elastography in U.S. adults using supervised and unsupervised machine learning models: An analysis of the National Health and Nutrition Examination Survey, 2017-2020
BMIN503/EPID600 Final Project
1 Overview
Using NHANES data, we aim to predict the determinants of liver steatosis and fibrosis (using the publically available fibroscan data). In addition, we will also learn to train a machine learning model to identify variables that can best predict the occurence of fibrosis. .
2 Introduction
Metabolic dysfunction-associated steatotic liver disease (MASLD) is prevalent in 30% of the US population and is strongly associated with the presence of cardiometabolic risk factors like obesity, type 2 diabetes, hypertension and dyslipidemia. Given that 1% of patients will develop cirrhosis, it is imperative to identify preventable independent variables that may influence its occurrence. We aimed to predict the determinants of liver steatosis and fibrosis and train a machine learning models to identify variables that can best predict the occurrence of fibrosis.
3 Methods
We will be using NHANES data to assess the determinants of advanced fibrosis from the link https://wwwn.cdc.gov/nchs/nhanes/continuousnhanes/default.aspx?Cycle=2017-2020
From the multiple data sets availabe from 2017-2020, we will be using the following files for the following: 1) demo_data; Demographic data 2) hepq_data; Hepatitis questionnaire data 3) lab_data; Lab data 4) dmq_data; dmq (diabetes questionnaire) data 5) a1c_data; a1c (diabetes lab) data 6) hepb_data; hepatitis b data 7) hepc_data; Hepatitis c data 8) fibroscan_data; Fibroscan (firbous elastography) data 9) insurance_data; insurance data 10)alcohol_data; Alcohol data
The study plan will comprise of
1) Identifying cases and controls using the fibroscan data
2) Use logistic regression models to identify variables that are associated with cases
3)create a supervised machine learning model to predict the occurence of steatosis
4) Plotting AUC curves for the same
6) create an unsupervised machine model (Kmeans clustering) and plot cases vs controls
Install packages
Load packages
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✔ ggplot2 3.4.4 ✔ tibble 3.2.1
✔ lubridate 1.9.3 ✔ tidyr 1.3.0
✔ purrr 1.0.2
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ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(modelsummary)
library(dplyr)
library(broom)
library(ggplot2)
library(dplyr)
library(haven) #required to read XPT files
library(tidyr)
library(kernlab)
Attaching package: 'kernlab'
The following object is masked from 'package:purrr':
cross
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alphalibrary(randomForest)randomForest 4.7-1.1
Type rfNews() to see new features/changes/bug fixes.
Attaching package: 'randomForest'
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marginlibrary(glmnet)Loading required package: Matrix
Attaching package: 'Matrix'
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expand, pack, unpack
Loaded glmnet 4.1-8library(tidymodels)── Attaching packages ────────────────────────────────────── tidymodels 1.1.1 ──
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✔ infer 1.0.5 ✔ tune 1.1.2
✔ modeldata 1.2.0 ✔ workflows 1.1.3
✔ parsnip 1.1.1 ✔ workflowsets 1.0.1
✔ recipes 1.0.8 ✔ yardstick 1.2.0
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• Use suppressPackageStartupMessages() to eliminate package startup messagestidymodels_prefer()
library(dotwhisker)
library(vip)
library(Rtsne)
library(cowplot)
library("ggdendro")
library(statsExpressions)
library(ggstatsplot)You can cite this package as:
Patil, I. (2021). Visualizations with statistical details: The 'ggstatsplot' approach.
Journal of Open Source Software, 6(61), 3167, doi:10.21105/joss.03167##read XPT files
demo_data <- read_xpt("P_DEMO.XPT") |> data.frame("P_DEMO.XPT")
hepq_data <- read_xpt("P_HEQ.XPT") |> data.frame("P_HEQ.XPT")
lab_data <- read_xpt("P_BIOPRO.XPT") |> data.frame("P_BIOPRO.XPT")
dmq_data <- read_xpt("P_DIQ.XPT") |> data.frame("P_DIQ.XPT")
a1c_data <- read_xpt("P_GHB.XPT") |> data.frame("P_GHB.XPT")
hepb_data <- read_xpt("P_HEPBD.XPT") |> data.frame("P_HEPBD.XPT")
hepc_data <- read_xpt("P_HEPC.XPT") |> data.frame("P_HEPC.XPT")
fibroscan_data <- read_xpt("P_LUX.XPT") |> data.frame("P_LUX.XPT")
insurance_data <- read_xpt("P_HIQ.XPT") |> data.frame("P_HIQ.XPT")
alcohol_data <- read_xpt("P_ALQ.XPT") |> data.frame("P_ALQ.XPT")
bodymeasurements_data <- read_xpt("P_BMX.XPT") |> data.frame("P_BMX.XPT")
#Merge each of the tables to create one master data sheet. This has to happen step-wise
merged_df <- merge(demo_data, hepq_data, by = "SEQN")
merged_df <- merge(merged_df, hepb_data, by = "SEQN")
merged_df <- merge(merged_df, hepc_data, by = "SEQN")
merged_df <- merge(merged_df, lab_data, by = "SEQN")
merged_df <- merge(merged_df, dmq_data, by = "SEQN")
merged_df <- merge(merged_df, a1c_data, by = "SEQN")
merged_df <- merge(merged_df, fibroscan_data, by = "SEQN")
merged_df <- merge(merged_df, insurance_data, by = "SEQN")
merged_df <- merge(merged_df, alcohol_data, by = "SEQN")
merged_df <- merge(merged_df, bodymeasurements_data, by = "SEQN")Now to modify each of the variables names of interest accordingly
#Alcohol
merged_df$etoh <- merged_df$ALQ151 #1->Y, 2-> No, 7-> refused, 9-> ?, .-> Missing
#biomarkers (continuous variables)
merged_df$alt <- merged_df$LBXSATSI #Values .-> Missing
merged_df$alb <- merged_df$LBXSAL
merged_df$alp <- merged_df$LBXSAPSI
merged_df$ast <- merged_df$LBXSASSI
merged_df$urea <- merged_df$LBXSBU
merged_df$cr <- merged_df$LBXSCR
merged_df$ggt <- merged_df$LBXSGTSI
merged_df$ldh <- merged_df$LBXSLDSI
merged_df$na <- merged_df$LBXSNASI
merged_df$tbil <- merged_df$LBXSTB
merged_df$chol <- merged_df$LBXSCH
merged_df$tg <- merged_df$LBXSTR
#HepQ data
merged_df$hb_self_reported <- merged_df$HEQ010 #1 Yes, 2 No, 7 Refused, 9 ?, . missing)
merged_df$hb_self_reported_treated <- merged_df$HEQ020 #Same as above
merged_df$hc_self_reported <- merged_df$HEQ030
merged_df$hc_self_reported_treated <- merged_df$HEQ040
#HepB data
merged_df$hbcore_positive <- merged_df$LBXHBC #1 yes, 2 neg, 3 +/-, . missing
merged_df$hbsag_positive <- merged_df$LBDHBG #1 yes, 2 neg, 3 +/-, . missing
#HepC data
merged_df$hcrna <- merged_df$LBXHCR #1 yes, 2 neg, 3 neg HCAb
merged_df$hcab <- merged_df$LBDHCI # 1 yes, 2 neg, 3 neg screening , 4 pos HCVRNA, . missing
merged_df$hcgenotype <- merged_df$LBXHCG # 1 1a, 2 1b, 3 1a/b?, 4 2, 5 3, 6 4, 7 5, 8, 6, 9 1
#A1c data
merged_df$ha1c <- merged_df$LBXGH #2.8-16.2
#fibroscan data
merged_df$fibroscan_meanstiffness_kpa <- merged_df$LUXSMED
merged_df$fibroscan_stiffnessiqr <- merged_df$LUXSIQR
merged_df$fibroscan_cap <- merged_df$LUXCAPM
merged_df$hc_self_cpiqr <- merged_df$LUXCPIQR
#Insurance data
merged_df$insurance_covered <- merged_df$HIQ011 # 1 yes, 2 no, 7 refused, 9 ?, . missing
#Demographic data
merged_df$demo_gender <- merged_df$RIAGENDR #1 male, 2 female
merged_df$demo_age <- merged_df$RIDAGEYR # 0-79 and >80
merged_df$demo_race <- merged_df$RIDRETH3 # 1 Mexican american, 2 other hisp, 3 NH White, 4 NH black, 6 NH Asian, 7 other race
merged_df$demo_education <- merged_df$DMDEDUC2 #1 <9thgr, 2 9-11th gr, 3 HSGrad, 4 college, 5 college grad
#Body measures
merged_df$body_bmi <- merged_df$BMXBMI
#convert data type to factors / numerics
merged_df$hb_self_reported <- as.factor(merged_df$hb_self_reported)
merged_df$hb_self_reported_treated <- as.factor(merged_df$hb_self_reported_treated)
merged_df$hc_self_reported <- as.factor(merged_df$hc_self_reported)
merged_df$hc_self_reported_treated <- as.factor(merged_df$hc_self_reported_treated)
merged_df$hbcore_positive <- as.factor(merged_df$hbcore_positive)
merged_df$hbsag_positive <- as.factor(merged_df$hbsag_positive)
merged_df$hcrna <- as.factor(merged_df$hcrna)
merged_df$hcab <- as.factor(merged_df$hcab)
merged_df$hcgenotype <- as.factor(merged_df$hcgenotype )
merged_df$insurance_covered <- as.factor(merged_df$insurance_covered)
merged_df$demo_gender <- as.factor(merged_df$demo_gender)
merged_df$demo_race <- as.factor(merged_df$demo_race)
merged_df$demo_education <- as.factor(merged_df$demo_education)4 Definition of Phenotype
Cases:
1) Steatosis
Steatosis cut offs using fibroscan (https://pubmed.ncbi.nlm.nih.gov/30689971/) CAP value > 288
2) Cirrhosis
We will use a fibroscan mean liver stiffness measurement of >20 kPA for the definition of cirrhosis https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1856085/ https://journals.lww.com/hep/Fulltext/2023/05000/AASLD_Practice_Guidance_on_the_clinical_assessment.31.aspx>
Controls:
1) Steatosis controls: CAP < 288
2) Cirrhosis controls: Fibroscan <8kPA
Create columns that represent the phenotype
#Cirrhosis to 0 and 1 using fibroscan data
merged_df <- merged_df |> mutate(fibroscan_cirrhosis = ifelse(fibroscan_meanstiffness_kpa > 20, 1, 0))
#Steatosis to 0 an 1 using fibroscan data
merged_df <- merged_df |> mutate(fibroscan_steatosis = ifelse(merged_df$fibroscan_cap > 288, 1, 0))
merged_df$fibroscan_cirrhosis <- as.factor(merged_df$fibroscan_cirrhosis)
merged_df$fibroscan_steatosis <- as.factor(merged_df$fibroscan_steatosis)
#check data type
summary(merged_df$fibroscan_steatosis) #2888 patients with steatosis 0 1 NA's
5429 2888 648 summary(merged_df$fibroscan_cirrhosis) #142 patients with cirrhosis 0 1 NA's
8176 142 647 We will also truncate the table to only the columns of interest
df <- merged_df[, c("alt", "alb","alp", "ast", "urea", "cr", "ggt", "ldh", "na", "tbil", "chol", "tg", "etoh", "fibroscan_meanstiffness_kpa", "ha1c", "fibroscan_stiffnessiqr", "fibroscan_cap", "hc_self_cpiqr", "insurance_covered","demo_gender", "demo_age" , "demo_race", "demo_education", "body_bmi", "hb_self_reported", "hc_self_reported", "hc_self_reported", "hbcore_positive", "hcrna", "hcab", "fibroscan_steatosis", "fibroscan_cirrhosis")]
# we will have to remove columns hc_self_reported_treated, hb_self_reported_treated, hcgenotype, hbsag as these are the columns with the maximum number of missings
#We now remove all the missings
df <- na.omit(df)5 Results
6 Identifying variables associated with Steatosis
model_steatosis_binary <- glm(fibroscan_steatosis ~ alt + alb + alp + ast + urea + cr + ggt + ldh + na + tbil + chol + tg + etoh + ha1c + insurance_covered + demo_gender + demo_age + demo_race + demo_education + body_bmi, data = df, family = binomial)
summary(model_steatosis_binary)
Call:
glm(formula = fibroscan_steatosis ~ alt + alb + alp + ast + urea +
cr + ggt + ldh + na + tbil + chol + tg + etoh + ha1c + insurance_covered +
demo_gender + demo_age + demo_race + demo_education + body_bmi,
family = binomial, data = df)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.305e+01 1.971e+00 -6.620 3.58e-11 ***
alt 2.944e-02 3.892e-03 7.564 3.90e-14 ***
alb 3.368e-01 1.162e-01 2.898 0.003758 **
alp -2.500e-04 1.429e-03 -0.175 0.861165
ast -2.193e-02 5.341e-03 -4.105 4.04e-05 ***
urea -2.967e-02 7.143e-03 -4.154 3.27e-05 ***
cr 1.015e-01 8.848e-02 1.148 0.251119
ggt 1.510e-03 9.010e-04 1.676 0.093732 .
ldh -2.047e-03 1.126e-03 -1.818 0.069060 .
na 2.751e-02 1.295e-02 2.125 0.033619 *
tbil -4.607e-01 1.371e-01 -3.359 0.000782 ***
chol -5.913e-04 8.623e-04 -0.686 0.492863
tg 4.164e-03 4.470e-04 9.314 < 2e-16 ***
etoh -4.737e-02 7.426e-02 -0.638 0.523534
ha1c 3.191e-01 3.466e-02 9.209 < 2e-16 ***
insurance_covered2 -8.556e-02 9.763e-02 -0.876 0.380823
insurance_covered7 -9.607e+00 3.247e+02 -0.030 0.976400
insurance_covered9 5.976e-01 8.615e-01 0.694 0.487908
demo_gender2 -5.287e-01 7.762e-02 -6.812 9.64e-12 ***
demo_age 2.356e-02 2.472e-03 9.531 < 2e-16 ***
demo_race2 -6.194e-01 1.321e-01 -4.689 2.75e-06 ***
demo_race3 -5.681e-01 1.117e-01 -5.087 3.65e-07 ***
demo_race4 -1.264e+00 1.245e-01 -10.156 < 2e-16 ***
demo_race6 -1.600e-01 1.487e-01 -1.076 0.282128
demo_race7 -7.997e-01 1.747e-01 -4.576 4.73e-06 ***
demo_education2 2.656e-01 1.642e-01 1.617 0.105856
demo_education3 3.699e-01 1.490e-01 2.482 0.013054 *
demo_education4 3.976e-01 1.469e-01 2.706 0.006809 **
demo_education5 2.251e-01 1.533e-01 1.468 0.141977
demo_education7 2.234e+01 4.593e+02 0.049 0.961211
demo_education9 4.558e-01 1.081e+00 0.422 0.673381
body_bmi 1.625e-01 6.169e-03 26.348 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 8003.6 on 6118 degrees of freedom
Residual deviance: 5815.0 on 6087 degrees of freedom
AIC: 5879
Number of Fisher Scoring iterations: 11significant_results_steatosis_binary <- tidy(model_steatosis_binary)|> filter(p.value < 0.05) |> arrange(p.value) |> mutate(Odds_Ratio = exp(estimate))
table(df$fibroscan_steatosis)
0 1
3910 2209 #How does the strongest variable associate with the outcome? # BMI
#PLOT
plot1 <- ggplot(df, aes(x = fibroscan_steatosis, y = body_bmi)) +
geom_violin(aes(fill = fibroscan_steatosis)) +
geom_boxplot(width = 0.1, alpha = 0.2)
plot1
summary(df$body_bmi) Min. 1st Qu. Median Mean 3rd Qu. Max.
14.60 25.00 28.90 30.15 33.90 92.30 ggbetweenstats(
data = df,
x = fibroscan_steatosis,
y = body_bmi,
title = "Steatosis vs BMI ")
As a continuous variable
model_steatosis_continuous <- glm(fibroscan_cap ~ alt + alb + alp + ast + urea + cr + ggt + ldh + na + tbil + chol + tg + etoh + ha1c + insurance_covered + demo_gender + demo_age + demo_race + demo_education + body_bmi, data = df)
significant_results_steatosis_continuous <- tidy(model_steatosis_continuous)|> filter(p.value < 0.05) |> arrange(p.value) |> mutate(Odds_Ratio = exp(estimate))
significant_results_steatosis_continuous# A tibble: 20 × 6
term estimate std.error statistic p.value Odds_Ratio
<chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 body_bmi 4.23 0.0917 46.2 0 6.90e+ 1
2 demo_age 0.639 0.0431 14.8 8.55e-49 1.89e+ 0
3 tg 0.111 0.00776 14.2 2.42e-45 1.12e+ 0
4 ha1c 7.64 0.626 12.2 7.63e-34 2.08e+ 3
5 demo_race4 -26.9 2.29 -11.8 1.34e-31 2.03e-12
6 alt 0.571 0.0613 9.32 1.63e-20 1.77e+ 0
7 demo_gender2 -13.1 1.41 -9.31 1.71e-20 2.07e- 6
8 urea -0.861 0.133 -6.47 1.07e-10 4.23e- 1
9 demo_race3 -11.0 2.13 -5.15 2.74e- 7 1.70e- 5
10 alb 9.95 2.11 4.70 2.61e- 6 2.09e+ 4
11 ast -0.355 0.0813 -4.37 1.26e- 5 7.01e- 1
12 demo_race2 -10.8 2.54 -4.26 2.10e- 5 2.03e- 5
13 demo_race7 -12.3 3.25 -3.78 1.58e- 4 4.64e- 6
14 demo_education3 10.2 2.86 3.57 3.54e- 4 2.80e+ 4
15 demo_education4 9.70 2.82 3.44 5.92e- 4 1.63e+ 4
16 tbil -7.39 2.33 -3.17 1.53e- 3 6.19e- 4
17 na 0.691 0.240 2.88 3.98e- 3 2.00e+ 0
18 demo_education2 8.63 3.15 2.74 6.12e- 3 5.62e+ 3
19 demo_education5 6.64 2.94 2.26 2.40e- 2 7.65e+ 2
20 ldh -0.0393 0.0197 -1.99 4.64e- 2 9.61e- 1#How does the strongest variable associate with the outcome? # BMI
#PLOT
plot2 <- ggplot(df, aes(x = body_bmi, y = fibroscan_cap)) + geom_point()+
geom_smooth(method = "lm")
plot2`geom_smooth()` using formula = 'y ~ x'
7 Identifying variables associated with Cirrhosis
table(df$hbcore_positive)
1 2 3
449 5670 0 model_cirrhosis_binary <- glm(fibroscan_cirrhosis ~ alt + alb + alp + ast + urea + cr + ggt + ldh + na + tbil + chol + tg + etoh + ha1c + insurance_covered + demo_gender + demo_age + demo_race + demo_education + body_bmi + hcab + hbcore_positive + hcrna, data = df, family = binomial)
summary(model_cirrhosis_binary)
Call:
glm(formula = fibroscan_cirrhosis ~ alt + alb + alp + ast + urea +
cr + ggt + ldh + na + tbil + chol + tg + etoh + ha1c + insurance_covered +
demo_gender + demo_age + demo_race + demo_education + body_bmi +
hcab + hbcore_positive + hcrna, family = binomial, data = df)
Coefficients: (2 not defined because of singularities)
Estimate Std. Error z value Pr(>|z|)
(Intercept) -5.661e+00 6.198e+00 -0.913 0.36104
alt -1.314e-02 6.022e-03 -2.183 0.02907 *
alb -1.476e+00 3.429e-01 -4.306 1.66e-05 ***
alp 7.308e-03 3.156e-03 2.315 0.02059 *
ast 2.390e-02 7.572e-03 3.156 0.00160 **
urea 1.063e-02 1.687e-02 0.630 0.52874
cr 4.006e-04 1.844e-01 0.002 0.99827
ggt 1.956e-03 1.528e-03 1.280 0.20053
ldh 5.765e-03 2.190e-03 2.633 0.00847 **
na 5.326e-03 4.113e-02 0.129 0.89697
tbil 1.381e+00 2.957e-01 4.670 3.01e-06 ***
chol -2.711e-03 2.968e-03 -0.913 0.36116
tg 2.411e-03 9.535e-04 2.529 0.01144 *
etoh -1.246e-02 2.530e-01 -0.049 0.96074
ha1c 6.279e-02 8.131e-02 0.772 0.43996
insurance_covered2 -6.664e-01 3.926e-01 -1.697 0.08960 .
insurance_covered7 -1.636e+01 2.400e+03 -0.007 0.99456
insurance_covered9 -1.056e+01 8.873e+02 -0.012 0.99050
demo_gender2 -1.348e+00 2.740e-01 -4.920 8.67e-07 ***
demo_age 1.147e-02 8.543e-03 1.342 0.17945
demo_race2 6.609e-01 4.979e-01 1.327 0.18441
demo_race3 5.031e-01 4.400e-01 1.143 0.25287
demo_race4 1.564e-01 4.684e-01 0.334 0.73848
demo_race6 1.046e+00 5.892e-01 1.775 0.07597 .
demo_race7 -2.647e-02 6.626e-01 -0.040 0.96813
demo_education2 -1.735e-01 5.436e-01 -0.319 0.74960
demo_education3 -1.956e-01 5.020e-01 -0.390 0.69684
demo_education4 9.847e-03 4.848e-01 0.020 0.98380
demo_education5 -3.891e-01 5.383e-01 -0.723 0.46973
demo_education7 4.764e+00 3.393e+03 0.001 0.99888
demo_education9 -1.231e+01 1.171e+03 -0.011 0.99161
body_bmi 1.207e-01 1.197e-02 10.082 < 2e-16 ***
hcab2 -3.258e-01 1.225e+00 -0.266 0.79030
hcab3 -1.127e+00 6.280e-01 -1.794 0.07277 .
hcab4 9.067e-01 7.580e-01 1.196 0.23165
hbcore_positive2 2.805e-01 4.274e-01 0.656 0.51164
hcrna2 NA NA NA NA
hcrna3 NA NA NA NA
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 1094.11 on 6118 degrees of freedom
Residual deviance: 758.91 on 6083 degrees of freedom
AIC: 830.91
Number of Fisher Scoring iterations: 15significant_results_cirrhosis_binary <- tidy(model_cirrhosis_binary)|> filter(p.value < 0.05) |> arrange(p.value) |> mutate(Odds_Ratio = exp(estimate))
significant_results_cirrhosis_binary# A tibble: 9 × 6
term estimate std.error statistic p.value Odds_Ratio
<chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 body_bmi 0.121 0.0120 10.1 6.63e-24 1.13
2 demo_gender2 -1.35 0.274 -4.92 8.67e- 7 0.260
3 tbil 1.38 0.296 4.67 3.01e- 6 3.98
4 alb -1.48 0.343 -4.31 1.66e- 5 0.228
5 ast 0.0239 0.00757 3.16 1.60e- 3 1.02
6 ldh 0.00577 0.00219 2.63 8.47e- 3 1.01
7 tg 0.00241 0.000953 2.53 1.14e- 2 1.00
8 alp 0.00731 0.00316 2.32 2.06e- 2 1.01
9 alt -0.0131 0.00602 -2.18 2.91e- 2 0.987#How does the strongest variable associate with the outcome? \# BMI
#PLOT
plot10 <- ggplot(data=df, aes(x = fibroscan_cirrhosis, y = body_bmi)) +
geom_violin(aes(fill = fibroscan_cirrhosis)) +
geom_boxplot(width = 0.1, alpha = 0.2)
plot10
ggbetweenstats(
data = df,
x = fibroscan_steatosis,
y = body_bmi,
title = "Steatosis vs BMI ")
As a continuous variable
model_cirrhosis_continuous <- glm(fibroscan_meanstiffness_kpa ~ alt + alb + alp + ast + urea + cr + ggt + ldh + na + tbil + chol + tg + etoh + ha1c + insurance_covered + demo_gender + demo_age + demo_race + demo_education + body_bmi + hcab + hbcore_positive + hcrna, data = df)
significant_results_cirrhosis_continuous <- tidy(model_cirrhosis_continuous)|> filter(p.value < 0.05) |> arrange(p.value) |> mutate(Odds_Ratio = exp(estimate))
significant_results_cirrhosis_continuous# A tibble: 13 × 6
term estimate std.error statistic p.value Odds_Ratio
<chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 body_bmi 0.196 0.00965 20.3 4.46e-89 1.22
2 ast 0.0672 0.00860 7.82 6.18e-15 1.07
3 tbil 1.45 0.245 5.92 3.47e- 9 4.26
4 ggt 0.00899 0.00169 5.30 1.17e- 7 1.01
5 demo_gender2 -0.770 0.148 -5.21 1.97e- 7 0.463
6 alt -0.0326 0.00645 -5.06 4.38e- 7 0.968
7 hcab3 -2.32 0.566 -4.10 4.15e- 5 0.0981
8 ha1c 0.247 0.0658 3.76 1.74e- 4 1.28
9 chol -0.00525 0.00169 -3.11 1.90e- 3 0.995
10 hcab2 -2.70 1.10 -2.45 1.44e- 2 0.0673
11 alb -0.515 0.223 -2.31 2.09e- 2 0.597
12 alp 0.00625 0.00276 2.26 2.38e- 2 1.01
13 ldh 0.00437 0.00208 2.11 3.52e- 2 1.00 #How does the strongest variable associate with the outcome? # BMI
#PLOT to see the number of hcrna
plot11 <- ggplot(df, aes(x = body_bmi, y = fibroscan_meanstiffness_kpa, color=hcrna)) + geom_point()+
geom_smooth(method = "lm")
plot11`geom_smooth()` using formula = 'y ~ x'
#PLOT to see the numebr of hb
plot12 <- ggplot(df, aes(x = body_bmi, y = fibroscan_meanstiffness_kpa, color=hbcore_positive)) + geom_point()+
geom_smooth(method = "lm")
plot12`geom_smooth()` using formula = 'y ~ x'
8 Supervised machine learning using Random Forest Model to assess most important factors/GINI in Steatosis
For this we will have to convert the cases to 1 and controls to 0 as the “truth” argument of the predictor variable regonizes “Cases” and “Controls” best
#We will convert 1-> Cases and 0-> Controls
#Steatosis
df<- df |>
mutate(fibroscan_steatosis = ifelse(fibroscan_steatosis == 1, "Cases", "Controls"))
table(df$fibroscan_steatosis)
Cases Controls
2209 3910 df$fibroscan_steatosis <- as.factor(df$fibroscan_steatosis)create a new data frame without any other fibroscan data except for fibroscan_steatosis and fibroscan_cirrhosis as they will automatically serve as a predictor
df <- subset(df, select = -c(fibroscan_meanstiffness_kpa, fibroscan_cap, fibroscan_stiffnessiqr))#Random forest model
rf_cls_spec <-
rand_forest(trees = 1000, min_n = 5) |>
set_engine("randomForest", importance = TRUE) |>
set_mode("classification")
rf_cls_specRandom Forest Model Specification (classification)
Main Arguments:
trees = 1000
min_n = 5
Engine-Specific Arguments:
importance = TRUE
Computational engine: randomForest rf_cls_fit_steatosis <- rf_cls_spec |>
fit(fibroscan_steatosis ~ alt + alb + alp + ast + urea + cr + ggt + ldh + na + tbil + chol + tg + etoh + ha1c + insurance_covered + demo_gender + demo_age + demo_race + demo_education + body_bmi, data = df)
rf_cls_fit_steatosisparsnip model object
Call:
randomForest(x = maybe_data_frame(x), y = y, ntree = ~1000, nodesize = min_rows(~5, x), importance = ~TRUE)
Type of random forest: classification
Number of trees: 1000
No. of variables tried at each split: 4
OOB estimate of error rate: 23.09%
Confusion matrix:
Cases Controls class.error
Cases 1333 876 0.3965595
Controls 537 3373 0.1373402#for importance scores
rf_cls_fit_steatosis |>
extract_fit_engine() |>
importance() Cases Controls MeanDecreaseAccuracy MeanDecreaseGini
alt 45.4991169 23.64245431 53.4504034 170.478344
alb 12.2211201 4.74865057 12.5647942 80.293344
alp -1.2853395 11.69017412 8.7689564 111.643334
ast 7.9798444 19.72941214 23.2701939 92.229670
urea 7.5346294 9.22436835 12.6947060 85.900699
cr -1.7214956 22.17715928 18.5799727 114.903158
ggt 51.9074914 9.00310506 47.9341298 173.904832
ldh -0.1882709 12.53978022 10.1661016 110.038608
na -1.7859580 0.07608038 -1.0953860 67.431606
tbil 1.6603410 1.99596704 2.6367716 56.242832
chol -3.0923497 13.41245080 8.7738474 117.524927
tg 54.4507920 26.47363956 58.7478758 244.696868
etoh -1.3242844 -0.71342240 -1.4184659 11.316399
ha1c 45.9624279 39.91553997 58.7332334 202.650729
insurance_covered -1.6647670 0.44609323 -0.7602302 9.688696
demo_gender 5.9166646 18.94318936 20.2117152 22.099288
demo_age 15.1930408 15.29898209 23.6954579 120.232331
demo_race 18.4898717 14.32628778 24.4222718 97.649092
demo_education -0.6198460 5.55791484 3.8608468 66.995170
body_bmi 132.6189133 91.47132887 144.0097706 508.527229#to plot MeanDecreaseGini
plot3 <- rf_cls_fit_steatosis |>
extract_fit_engine() |>
vip()
plot3 
#save
rf.predicted.steatosis <- bind_cols(
truth = df$fibroscan_steatosis,
predict(rf_cls_fit_steatosis, df),
predict(rf_cls_fit_steatosis, df, type = "prob")
)
rf.predicted.steatosis# A tibble: 6,119 × 4
truth .pred_class .pred_Cases .pred_Controls
<fct> <fct> <dbl> <dbl>
1 Controls Controls 0.114 0.886
2 Cases Cases 0.612 0.388
3 Controls Controls 0.073 0.927
4 Controls Controls 0.208 0.792
5 Cases Cases 0.693 0.307
6 Cases Cases 0.766 0.234
7 Controls Controls 0.236 0.764
8 Cases Cases 0.747 0.253
9 Controls Controls 0.038 0.962
10 Cases Cases 0.895 0.105
# ℹ 6,109 more rows#RF plots
plot4 <- autoplot(roc_curve(rf.predicted.steatosis,
truth, .pred_Cases ))
plot4 
plot5 <- roc_auc(rf.predicted.steatosis,
truth, .pred_Cases )
plot5# A tibble: 1 × 3
.metric .estimator .estimate
<chr> <chr> <dbl>
1 roc_auc binary 1.00For obtaining 10-fold cross validation classification vectors for the model
set.seed(1234)
data.split <- initial_split(df,
strata = fibroscan_steatosis,
prop = 0.80)
data.split<Training/Testing/Total>
<4895/1224/6119>data.train <- training(data.split)
data.test <- testing(data.split)Training based on RF model
rf_cls_fit_train<- rf_cls_spec |>
fit(fibroscan_steatosis ~ ., data = data.train)
rf_cls_fit_trainparsnip model object
Call:
randomForest(x = maybe_data_frame(x), y = y, ntree = ~1000, nodesize = min_rows(~5, x), importance = ~TRUE)
Type of random forest: classification
Number of trees: 1000
No. of variables tried at each split: 5
OOB estimate of error rate: 22.64%
Confusion matrix:
Cases Controls class.error
Cases 1098 669 0.3786078
Controls 439 2689 0.1403453Testing based on RF model
data.rf.pred.values.test <- bind_cols(
truth = data.test$fibroscan_steatosis,
predict(rf_cls_fit_train, data.test),
predict(rf_cls_fit_train, data.test, type = "prob")
)
data.rf.pred.values.test# A tibble: 1,224 × 4
truth .pred_class .pred_Cases .pred_Controls
<fct> <fct> <dbl> <dbl>
1 Cases Controls 0.208 0.792
2 Cases Cases 0.575 0.425
3 Cases Controls 0.473 0.527
4 Controls Controls 0.389 0.611
5 Controls Controls 0.085 0.915
6 Controls Cases 0.562 0.438
7 Cases Controls 0.358 0.642
8 Cases Cases 0.718 0.282
9 Controls Cases 0.509 0.491
10 Cases Cases 0.727 0.273
# ℹ 1,214 more rowsROC and AUC
plot6 <- autoplot(roc_curve(data.rf.pred.values.test,
truth, .pred_Cases))
plot6
plot7 <- roc_auc(data.rf.pred.values.test,
truth, .pred_Cases)
plot7# A tibble: 1 × 3
.metric .estimator .estimate
<chr> <chr> <dbl>
1 roc_auc binary 0.8379 Unsupervised machine learning using Kmeans clustering in Steatosis
set.seed(1234)
df.kmeans <- kmeans(df[ , 1:24], 2)
df.kmeansK-means clustering with 2 clusters of sizes 995, 5124
Cluster means:
alt alb alp ast urea cr ggt ldh
1 29.18392 4.084121 82.52462 24.49648 15.97990 0.9291658 50.20201 157.3598
2 21.16608 4.064637 76.09719 21.39617 14.70258 0.9015925 28.89325 158.0911
na tbil chol tg etoh ha1c hc_self_cpiqr
1 140.1518 0.4215075 209.5337 286.6874 1.827136 6.250854 33.63618
2 140.6899 0.4695160 181.1401 105.3134 1.859875 5.754313 37.62627
insurance_covered demo_gender demo_age demo_race demo_education body_bmi
1 1.20000 1.361809 52.31960 3.204020 3.437186 31.91015
2 1.16491 1.516784 50.13661 3.418033 3.659251 29.80289
hb_self_reported hc_self_reported hc_self_reported.1
1 2.006030 2.009045 2.009045
2 2.020101 2.011905 2.011905
Clustering vector:
1 2 3 4 5 8 10 11 13 14 15 18 19 20 21 23
2 2 2 2 2 2 2 1 2 1 2 2 2 2 2 2
30 31 34 35 36 37 38 40 42 43 44 45 47 48 49 50
2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2
51 53 54 55 56 57 58 61 62 63 64 65 66 67 68 69
2 2 2 2 2 2 1 2 2 2 2 1 2 2 2 1
70 71 72 73 74 76 78 79 80 82 84 86 87 89 91 92
2 2 2 2 2 2 1 2 2 1 2 2 2 2 2 1
93 95 96 97 98 99 103 104 105 106 107 109 110 112 113 116
2 1 2 2 2 2 2 2 1 2 1 1 2 1 2 1
117 118 119 121 122 123 124 125 126 127 129 131 132 133 134 136
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
137 139 141 143 144 145 146 147 148 149 150 151 152 155 156 157
2 2 2 2 2 1 2 1 2 2 1 2 2 2 2 2
158 159 162 163 164 165 166 167 169 171 173 174 178 179 180 181
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
182 183 184 185 186 189 190 191 192 193 194 195 196 198 200 201
2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2
203 206 207 209 210 211 213 215 216 217 219 220 222 225 226 228
2 2 2 1 2 2 2 2 2 2 2 2 2 2 1 2
229 230 231 233 235 237 238 239 240 241 243 244 245 248 249 250
2 2 2 1 1 2 2 1 2 2 2 2 2 2 1 1
252 253 254 257 259 260 261 262 263 264 266 267 268 269 270 272
2 2 2 2 2 2 2 2 2 1 2 1 2 2 1 2
273 275 276 277 279 280 281 283 284 285 287 288 289 290 293 294
2 1 2 2 2 2 2 2 2 1 2 2 2 1 2 2
295 300 301 303 305 306 308 309 310 311 312 314 315 316 320 322
1 1 2 2 2 2 1 2 2 2 2 2 2 1 2 2
324 325 326 327 328 329 330 331 333 336 337 338 339 342 343 344
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
345 346 348 349 350 351 352 355 357 359 360 361 363 364 365 367
1 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2
368 372 374 375 376 377 380 382 383 384 387 388 389 390 392 395
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
396 397 399 400 401 402 403 406 408 409 410 411 412 413 414 415
2 2 2 2 2 2 2 1 2 1 2 1 2 2 2 2
416 417 418 419 420 421 422 424 425 426 427 428 429 430 431 435
1 2 2 2 2 1 2 1 2 2 2 2 2 2 2 2
436 437 438 441 443 444 445 446 447 449 450 452 455 457 458 459
2 1 1 2 2 1 2 2 2 2 2 2 2 1 2 2
460 461 462 463 464 465 467 468 470 472 473 474 475 476 477 478
1 2 2 1 1 2 2 1 2 2 2 2 2 1 2 2
479 480 481 482 483 484 485 486 487 488 489 490 491 495 497 498
1 2 1 2 2 2 1 2 2 1 2 2 2 2 2 2
500 501 503 505 506 507 508 511 512 513 514 516 517 518 519 524
2 2 1 2 2 2 2 2 2 2 2 2 2 2 1 2
526 527 528 531 532 533 534 535 536 538 539 540 541 542 544 546
2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2
548 553 557 558 559 561 562 563 564 565 566 567 568 569 570 571
2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2
572 573 574 575 576 578 579 580 581 583 585 586 587 589 590 591
1 2 2 2 2 2 1 1 2 2 2 2 1 2 2 2
592 594 595 596 597 598 599 600 602 603 605 607 608 609 610 611
2 2 1 2 2 2 2 2 1 2 2 2 2 2 1 1
612 613 614 616 617 618 621 622 623 624 625 628 629 631 632 634
1 2 2 2 2 1 2 2 2 2 2 2 1 1 2 2
635 636 638 639 640 642 643 645 647 649 650 651 652 655 656 659
2 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2
661 662 663 665 666 668 670 671 672 677 678 680 681 682 683 684
2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2
687 690 693 694 695 697 698 699 700 701 706 709 711 713 714 715
2 2 2 1 2 2 2 1 2 2 1 2 1 2 2 2
716 719 723 724 726 727 728 729 730 731 732 733 734 737 738 740
2 2 2 2 2 2 1 2 2 2 2 2 1 2 2 1
741 742 747 748 749 750 752 753 754 759 760 762 763 765 767 768
2 2 1 2 2 2 2 2 1 2 1 1 2 2 2 2
769 772 773 774 775 776 777 778 779 780 782 783 784 785 786 788
2 2 2 2 2 1 2 2 2 2 2 2 2 1 2 2
790 792 794 795 798 799 801 802 803 804 806 807 809 811 812 813
2 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2
814 815 818 819 820 821 822 824 825 827 829 830 832 833 834 836
2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2
838 840 843 844 847 850 852 855 856 857 858 861 863 865 866 868
2 2 2 2 1 2 2 1 2 2 2 2 2 2 1 2
871 872 873 874 876 877 878 880 881 883 884 885 888 889 891 893
2 2 2 1 2 2 2 1 2 1 2 2 2 2 1 2
894 895 896 897 898 900 902 904 905 906 910 911 915 916 919 920
1 2 2 2 2 2 1 2 1 2 2 2 2 1 2 2
922 923 925 926 928 930 931 932 935 937 939 940 942 943 944 946
2 2 2 1 2 2 2 1 1 2 1 2 1 2 1 1
947 948 949 950 951 952 954 956 957 959 961 963 964 965 968 970
1 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1
971 972 973 976 978 979 980 981 982 983 984 985 986 988 990 991
2 2 1 2 2 1 2 2 2 2 1 2 2 1 2 1
994 995 996 997 998 999 1002 1004 1005 1006 1008 1009 1010 1012 1013 1014
2 1 2 1 2 2 2 2 2 2 2 2 2 2 1 2
1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1026 1027 1030 1031 1032 1033
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
1035 1036 1039 1042 1043 1045 1046 1047 1049 1051 1054 1056 1057 1058 1060 1061
2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2
1062 1066 1067 1068 1069 1070 1071 1072 1073 1075 1076 1077 1078 1079 1080 1082
2 2 2 1 2 2 1 1 2 2 1 2 1 2 2 2
1083 1084 1086 1089 1090 1091 1092 1093 1094 1095 1097 1098 1100 1101 1103 1104
2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2
1105 1106 1107 1108 1112 1113 1114 1115 1116 1117 1118 1119 1121 1122 1123 1124
2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2
1127 1128 1130 1131 1132 1133 1134 1135 1136 1139 1140 1143 1144 1146 1147 1148
2 2 1 2 2 2 1 2 2 1 2 2 2 1 2 2
1150 1151 1152 1154 1155 1158 1159 1161 1162 1163 1164 1165 1168 1169 1171 1172
2 2 2 2 2 1 2 2 1 2 1 2 2 2 1 2
1173 1178 1180 1181 1182 1183 1185 1187 1188 1189 1191 1194 1195 1196 1197 1199
1 2 2 2 1 2 2 2 2 2 2 1 2 1 2 2
1202 1203 1204 1207 1210 1211 1217 1219 1220 1221 1222 1223 1224 1225 1226 1227
1 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1
1228 1229 1230 1231 1232 1233 1234 1235 1237 1238 1239 1240 1241 1243 1244 1245
2 2 2 2 2 2 2 1 1 2 2 2 2 1 2 2
1247 1248 1253 1254 1257 1258 1261 1262 1263 1264 1265 1267 1268 1269 1270 1271
2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2
1272 1273 1274 1275 1277 1278 1279 1280 1281 1283 1284 1286 1287 1288 1289 1290
2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1
1292 1293 1294 1295 1296 1297 1298 1300 1302 1304 1305 1306 1310 1311 1312 1313
1 2 2 2 2 2 2 2 2 2 2 2 1 2 2 1
1314 1315 1317 1319 1321 1322 1324 1325 1326 1327 1328 1329 1331 1333 1335 1336
2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2
1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1350 1351 1353 1354 1355 1356
2 2 2 2 1 2 1 2 2 2 2 2 2 2 2 2
1357 1358 1360 1361 1363 1364 1365 1366 1367 1368 1369 1370 1372 1373 1376 1377
2 2 2 1 1 2 2 2 2 1 2 2 2 2 2 2
1378 1379 1380 1381 1383 1385 1387 1388 1389 1393 1394 1395 1396 1397 1398 1399
2 2 1 2 1 2 2 2 2 2 2 2 2 2 2 2
1400 1401 1402 1403 1405 1408 1409 1410 1412 1413 1418 1419 1420 1421 1423 1427
2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2
1428 1429 1430 1431 1432 1435 1436 1437 1438 1440 1441 1442 1443 1444 1445 1446
2 2 2 2 2 2 2 1 2 2 2 2 1 2 2 2
1448 1449 1450 1453 1454 1455 1459 1460 1461 1463 1464 1465 1467 1468 1470 1475
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
1476 1477 1478 1479 1483 1484 1485 1486 1487 1489 1490 1491 1492 1494 1495 1496
1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2
1497 1499 1500 1503 1504 1505 1506 1507 1509 1510 1511 1512 1513 1514 1515 1516
2 2 2 2 2 2 2 2 2 1 2 2 2 1 2 2
1518 1519 1520 1521 1522 1523 1525 1526 1527 1528 1530 1531 1532 1533 1534 1535
2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2
1543 1545 1546 1547 1548 1550 1552 1554 1555 1559 1560 1561 1562 1563 1564 1566
2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 2
1567 1570 1571 1572 1573 1574 1577 1578 1579 1581 1583 1584 1586 1590 1591 1592
2 1 2 2 2 2 2 1 2 1 2 1 2 2 2 2
1593 1594 1595 1596 1597 1598 1599 1601 1602 1603 1605 1606 1607 1608 1609 1610
1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2
1611 1612 1614 1615 1616 1620 1623 1626 1628 1629 1630 1631 1633 1635 1636 1637
2 1 2 2 2 1 2 2 2 2 2 1 2 2 2 1
1638 1640 1642 1643 1644 1646 1647 1648 1650 1651 1652 1653 1654 1656 1657 1658
2 1 1 1 2 2 2 2 2 1 2 2 2 1 2 2
1663 1664 1667 1669 1670 1671 1673 1674 1675 1676 1677 1678 1680 1681 1682 1683
2 1 2 2 2 1 2 2 2 2 2 2 2 2 2 2
1684 1687 1688 1689 1690 1692 1693 1695 1697 1698 1700 1701 1702 1705 1706 1707
2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 1
1708 1709 1711 1713 1718 1719 1721 1722 1723 1724 1725 1728 1729 1730 1733 1734
2 2 1 2 2 2 2 2 2 2 2 2 2 1 1 2
1735 1737 1738 1739 1740 1741 1742 1744 1745 1746 1747 1748 1749 1751 1753 1755
2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2
1756 1757 1758 1759 1760 1761 1762 1763 1768 1769 1770 1771 1772 1773 1774 1775
2 1 2 2 2 2 2 2 2 1 2 2 1 2 2 2
1776 1777 1778 1780 1781 1782 1783 1784 1785 1786 1787 1788 1791 1792 1793 1796
1 2 2 1 2 2 2 2 2 2 2 2 2 2 1 2
1797 1801 1803 1804 1807 1809 1810 1813 1814 1816 1818 1819 1821 1822 1826 1827
2 2 2 1 2 2 1 1 2 2 2 2 2 2 2 2
1828 1829 1830 1832 1833 1836 1837 1839 1844 1847 1850 1851 1855 1856 1857 1858
2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 1
1860 1861 1862 1863 1864 1867 1868 1870 1873 1874 1875 1876 1877 1878 1879 1882
2 1 2 1 2 2 1 2 2 2 2 2 2 2 2 2
1883 1885 1887 1888 1889 1890 1891 1892 1893 1894 1895 1897 1898 1900 1903 1904
2 1 1 1 2 2 2 1 2 2 2 1 2 2 2 2
1905 1906 1908 1910 1911 1912 1913 1914 1917 1918 1920 1921 1922 1923 1924 1925
2 2 1 2 1 2 2 2 2 2 2 2 1 2 2 2
1926 1929 1930 1931 1932 1935 1936 1937 1938 1939 1942 1943 1944 1945 1946 1947
2 2 2 2 1 1 1 2 2 2 1 2 2 2 1 2
1949 1950 1951 1952 1953 1954 1955 1956 1957 1959 1960 1962 1963 1964 1966 1969
2 2 2 2 2 1 2 1 1 2 2 2 2 2 2 2
1970 1972 1973 1975 1976 1977 1978 1980 1981 1982 1987 1990 1991 1992 1993 1994
2 2 2 2 1 2 2 2 1 2 1 1 1 2 2 2
1995 1996 1997 1998 1999 2000 2002 2003 2004 2005 2006 2007 2009 2010 2011 2012
1 1 2 2 2 2 1 2 2 2 2 2 1 2 2 2
2013 2014 2015 2016 2018 2019 2020 2021 2022 2023 2026 2027 2028 2029 2030 2031
2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2
2032 2034 2035 2036 2037 2038 2039 2041 2042 2043 2044 2045 2046 2047 2048 2049
2 2 1 2 2 2 2 2 2 2 2 2 2 2 1 2
2050 2051 2052 2054 2056 2057 2059 2060 2063 2064 2065 2067 2068 2071 2074 2075
1 2 1 2 2 2 2 2 2 2 2 2 1 2 2 2
2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2087 2089 2091 2094 2095 2096
2 1 2 2 2 2 1 2 2 1 2 2 2 2 2 1
2097 2099 2100 2102 2103 2105 2106 2108 2109 2110 2112 2113 2115 2116 2117 2118
2 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2
2119 2120 2121 2122 2123 2124 2125 2126 2127 2129 2130 2132 2133 2134 2135 2137
2 2 1 2 1 2 2 1 2 2 2 1 2 2 2 2
2139 2142 2144 2148 2152 2154 2156 2157 2158 2161 2163 2165 2166 2169 2170 2171
2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2
2172 2174 2175 2176 2177 2178 2181 2182 2183 2184 2185 2186 2187 2188 2190 2191
1 2 2 2 1 2 1 1 2 1 2 2 2 1 2 2
2193 2194 2195 2196 2197 2198 2199 2200 2201 2203 2207 2209 2211 2212 2213 2214
2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2
2215 2216 2217 2218 2221 2222 2223 2224 2225 2226 2228 2229 2230 2231 2232 2233
2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2
2235 2236 2237 2239 2240 2242 2243 2244 2247 2248 2249 2250 2251 2252 2254 2255
2 2 2 2 1 2 2 2 2 2 2 1 2 1 1 1
2256 2257 2258 2259 2260 2261 2262 2263 2264 2265 2266 2267 2270 2271 2272 2273
2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2
2274 2276 2278 2279 2280 2283 2284 2285 2286 2287 2288 2291 2294 2297 2298 2299
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1
2300 2302 2303 2304 2305 2309 2310 2311 2314 2316 2319 2320 2321 2323 2324 2325
1 2 1 2 2 2 2 2 2 2 2 2 2 1 2 2
2327 2328 2329 2330 2331 2332 2333 2334 2335 2336 2338 2339 2340 2342 2344 2345
2 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2
2346 2348 2351 2353 2354 2355 2356 2357 2359 2360 2361 2363 2364 2365 2366 2369
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
2370 2372 2373 2374 2375 2376 2377 2378 2379 2380 2382 2383 2384 2385 2386 2387
2 2 2 1 2 2 2 1 1 2 2 2 2 2 2 2
2388 2391 2392 2393 2394 2395 2398 2400 2402 2403 2405 2406 2407 2410 2411 2412
2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 1
2413 2414 2415 2418 2421 2424 2425 2426 2427 2428 2429 2433 2434 2435 2438 2439
2 2 2 2 2 1 2 2 1 2 1 1 2 1 2 2
2440 2441 2442 2443 2445 2447 2448 2449 2450 2452 2453 2454 2455 2456 2457 2458
1 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2
2460 2461 2462 2463 2464 2465 2466 2467 2471 2472 2474 2476 2477 2478 2479 2480
2 2 2 2 2 2 2 2 2 1 2 1 2 2 2 2
2481 2482 2483 2484 2485 2486 2487 2488 2491 2493 2494 2497 2498 2499 2500 2501
2 1 2 1 2 1 1 2 2 2 2 2 2 2 1 2
2502 2506 2508 2509 2510 2511 2513 2514 2515 2517 2518 2520 2521 2522 2524 2525
1 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2
2526 2527 2529 2530 2531 2533 2536 2538 2539 2540 2542 2543 2547 2548 2549 2551
2 2 2 1 2 2 1 2 2 2 2 2 2 2 2 2
2552 2553 2554 2559 2561 2563 2564 2567 2568 2570 2572 2573 2574 2575 2576 2577
2 2 2 2 2 2 2 2 1 2 2 2 1 2 2 2
2578 2579 2580 2581 2584 2586 2587 2588 2590 2591 2593 2596 2597 2598 2599 2602
2 2 1 2 2 2 2 2 2 2 2 1 2 2 2 2
2603 2605 2606 2608 2609 2611 2612 2614 2615 2616 2617 2619 2620 2622 2623 2624
2 2 2 2 2 2 1 2 2 2 2 2 1 1 2 1
2625 2626 2628 2629 2630 2631 2633 2634 2635 2636 2637 2638 2639 2642 2643 2644
1 1 2 2 2 2 1 2 1 2 2 2 1 2 2 2
2645 2648 2649 2652 2653 2655 2657 2662 2663 2664 2665 2669 2671 2672 2674 2675
2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 1
2676 2677 2678 2679 2681 2682 2684 2685 2688 2689 2690 2691 2692 2693 2697 2699
1 1 1 2 2 2 2 2 2 2 2 2 2 1 2 1
2701 2703 2705 2707 2708 2710 2711 2712 2714 2715 2716 2717 2718 2719 2721 2722
2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2
2724 2725 2726 2727 2728 2731 2732 2733 2734 2735 2736 2738 2739 2741 2742 2745
1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
2746 2748 2750 2752 2755 2756 2757 2758 2760 2761 2762 2763 2764 2765 2767 2768
2 2 2 1 2 2 2 1 1 2 2 2 2 2 1 1
2770 2774 2776 2777 2778 2779 2780 2781 2782 2783 2785 2786 2787 2788 2789 2790
2 2 2 2 2 2 2 2 1 2 1 2 1 2 2 2
2791 2792 2797 2798 2799 2800 2801 2802 2804 2806 2807 2808 2809 2810 2811 2812
2 2 1 2 2 2 1 2 2 2 2 2 2 1 2 2
2813 2814 2815 2816 2817 2818 2819 2820 2823 2824 2825 2826 2827 2828 2829 2830
1 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2
2832 2833 2835 2837 2840 2841 2842 2844 2845 2846 2847 2849 2851 2852 2853 2854
2 2 2 1 2 2 2 2 2 1 2 2 2 1 2 1
2855 2856 2857 2858 2859 2861 2862 2864 2865 2866 2867 2871 2872 2875 2876 2877
2 1 2 1 2 1 2 2 2 2 2 2 1 1 2 2
2879 2880 2881 2882 2884 2885 2886 2887 2890 2891 2892 2893 2896 2897 2898 2899
1 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2
2901 2902 2905 2906 2907 2908 2909 2911 2912 2914 2916 2917 2918 2919 2920 2924
1 1 2 1 2 2 2 2 2 2 2 2 2 2 1 2
2926 2928 2930 2931 2932 2933 2934 2935 2936 2938 2940 2942 2944 2945 2947 2949
2 2 2 2 2 2 2 1 2 2 1 1 2 2 2 2
2950 2953 2955 2956 2957 2959 2960 2962 2965 2966 2968 2969 2971 2972 2973 2975
2 1 2 2 1 2 1 2 2 2 2 2 2 2 2 2
2976 2977 2979 2980 2981 2983 2984 2985 2986 2988 2990 2991 2992 2993 2998 3002
2 2 2 1 1 2 2 2 1 2 2 2 2 2 2 2
3004 3007 3008 3009 3011 3012 3013 3014 3015 3016 3018 3020 3021 3022 3023 3024
2 2 1 2 2 2 2 2 2 2 1 2 2 2 2 2
3025 3027 3029 3030 3032 3034 3037 3038 3044 3045 3047 3048 3053 3055 3056 3057
1 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2
3058 3059 3060 3061 3062 3066 3067 3068 3070 3071 3072 3073 3077 3078 3080 3081
2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2
3082 3084 3087 3088 3092 3094 3095 3096 3097 3099 3100 3102 3104 3105 3106 3107
1 1 1 1 2 2 2 2 2 1 2 2 2 2 2 2
3108 3110 3112 3114 3115 3117 3119 3122 3124 3126 3127 3128 3129 3130 3131 3132
1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 1
3134 3135 3137 3138 3139 3140 3143 3146 3147 3148 3149 3152 3153 3154 3155 3156
2 2 2 1 2 2 2 2 2 2 1 2 1 2 1 2
3157 3158 3161 3163 3166 3168 3170 3171 3172 3173 3174 3176 3177 3178 3182 3184
1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2
3185 3186 3187 3188 3190 3191 3192 3194 3195 3196 3197 3198 3199 3200 3202 3204
1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2
3205 3207 3208 3209 3210 3212 3216 3217 3218 3219 3220 3221 3222 3223 3224 3225
2 2 2 2 2 1 2 1 1 2 2 2 2 2 2 2
3226 3227 3228 3230 3233 3234 3236 3237 3238 3239 3240 3241 3242 3244 3245 3246
2 2 2 2 2 1 2 2 2 2 1 2 2 2 2 2
3247 3249 3251 3252 3254 3257 3259 3261 3262 3264 3265 3266 3267 3268 3269 3272
2 1 2 2 2 2 2 2 2 2 2 2 1 2 2 2
3273 3274 3276 3277 3279 3280 3283 3285 3286 3287 3288 3289 3290 3291 3292 3293
2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1
3294 3295 3297 3299 3300 3301 3302 3304 3305 3307 3308 3310 3311 3314 3315 3318
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
3320 3321 3322 3325 3327 3328 3330 3331 3332 3334 3335 3336 3337 3339 3341 3342
2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 1
3343 3345 3346 3348 3349 3350 3351 3353 3355 3356 3357 3358 3359 3360 3361 3362
2 2 2 2 2 2 2 1 1 2 2 2 2 1 2 2
3363 3366 3367 3368 3369 3371 3372 3373 3374 3375 3377 3378 3380 3381 3384 3386
2 2 2 2 2 2 1 2 2 2 1 2 2 2 2 2
3387 3388 3389 3390 3391 3392 3393 3394 3396 3397 3398 3399 3400 3402 3403 3405
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
3407 3408 3409 3410 3411 3413 3415 3416 3417 3418 3419 3420 3421 3423 3424 3427
1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 1
3431 3432 3433 3434 3435 3436 3437 3438 3439 3440 3441 3442 3445 3446 3448 3449
2 2 2 1 2 1 2 2 2 2 2 2 2 2 2 1
3450 3451 3453 3454 3456 3457 3459 3460 3461 3462 3464 3465 3466 3467 3469 3470
2 2 2 1 2 2 2 1 2 2 2 2 2 2 2 2
3472 3474 3475 3476 3477 3478 3480 3481 3482 3485 3486 3489 3490 3491 3493 3494
2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
3496 3497 3498 3499 3500 3501 3502 3503 3504 3507 3508 3511 3514 3517 3522 3523
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
3529 3532 3534 3535 3536 3537 3541 3542 3543 3545 3546 3547 3548 3550 3551 3552
2 2 2 1 2 2 2 1 2 2 1 2 1 2 2 2
3554 3556 3557 3559 3562 3563 3564 3568 3569 3570 3571 3572 3575 3577 3579 3580
2 2 2 2 1 2 1 2 2 2 1 1 1 2 2 2
3582 3585 3586 3587 3588 3589 3591 3592 3594 3595 3597 3598 3600 3601 3602 3603
1 2 2 2 2 2 1 2 1 2 2 2 2 2 2 1
3605 3606 3607 3609 3610 3612 3613 3614 3615 3616 3617 3620 3621 3622 3623 3624
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
3625 3627 3628 3630 3631 3632 3634 3635 3636 3637 3640 3644 3645 3646 3647 3648
2 2 2 2 2 2 1 2 2 1 2 2 2 2 2 2
3649 3650 3651 3652 3653 3654 3658 3659 3660 3662 3663 3665 3668 3670 3671 3672
2 1 2 2 1 2 2 2 2 2 2 2 2 2 2 1
3674 3675 3678 3679 3681 3684 3685 3687 3688 3689 3691 3692 3693 3694 3695 3696
2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 2
3697 3699 3700 3702 3704 3705 3706 3707 3709 3710 3711 3713 3714 3715 3716 3718
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
3719 3720 3723 3724 3725 3727 3728 3729 3733 3736 3737 3739 3740 3741 3742 3743
1 2 1 2 2 2 1 2 2 2 2 2 2 2 2 2
3746 3748 3750 3751 3752 3753 3754 3756 3757 3758 3759 3760 3762 3765 3767 3768
1 1 2 1 1 2 2 2 2 2 2 1 2 1 2 2
3770 3771 3772 3773 3777 3778 3779 3780 3781 3782 3784 3785 3786 3787 3789 3790
2 2 2 2 2 2 2 1 2 2 2 2 2 1 2 2
3793 3796 3797 3798 3799 3800 3801 3803 3806 3807 3809 3810 3812 3814 3815 3818
2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2
3819 3820 3821 3825 3827 3828 3829 3830 3831 3832 3834 3835 3836 3837 3838 3843
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
3844 3845 3846 3847 3849 3850 3851 3852 3854 3855 3856 3857 3859 3860 3861 3862
2 2 2 2 2 1 2 2 2 2 2 1 2 1 2 2
3863 3865 3867 3869 3870 3871 3873 3875 3877 3878 3879 3880 3881 3883 3884 3885
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
3886 3887 3888 3889 3890 3891 3892 3893 3897 3899 3900 3902 3903 3904 3905 3907
2 1 2 2 1 1 2 2 2 1 2 1 2 1 2 2
3908 3910 3911 3912 3913 3914 3916 3917 3919 3920 3921 3922 3923 3924 3925 3926
2 1 2 2 1 2 1 2 1 2 2 2 2 2 1 2
3927 3928 3929 3931 3933 3934 3935 3936 3938 3939 3940 3941 3944 3945 3946 3948
2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2
3949 3950 3951 3952 3954 3955 3956 3958 3961 3962 3963 3964 3967 3968 3969 3970
2 1 2 2 2 2 2 2 2 2 1 2 2 2 2 2
3971 3973 3974 3975 3976 3977 3978 3979 3981 3986 3987 3988 3989 3990 3991 3992
2 2 1 2 2 2 2 2 2 2 1 2 1 1 2 2
3996 3997 3998 3999 4000 4001 4002 4003 4004 4007 4008 4009 4010 4011 4012 4013
2 1 2 2 2 2 1 1 2 2 1 2 1 2 2 2
4015 4016 4018 4021 4022 4023 4025 4026 4027 4028 4030 4032 4033 4036 4037 4038
2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2
4040 4042 4043 4045 4048 4049 4051 4052 4054 4055 4056 4057 4059 4060 4061 4065
2 1 1 2 2 2 1 2 2 2 2 2 2 2 2 2
4067 4068 4069 4071 4074 4075 4076 4078 4079 4080 4081 4083 4085 4093 4094 4095
1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
4096 4097 4098 4099 4101 4102 4103 4105 4106 4107 4108 4109 4111 4112 4113 4115
1 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2
4116 4118 4119 4120 4121 4123 4125 4126 4127 4128 4130 4134 4136 4137 4138 4139
1 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2
4140 4141 4142 4143 4144 4145 4146 4147 4148 4149 4150 4151 4152 4153 4154 4158
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1
4159 4160 4163 4164 4166 4167 4168 4169 4171 4174 4175 4176 4177 4178 4179 4180
2 2 2 2 2 2 1 2 2 2 2 1 2 2 2 2
4181 4182 4184 4187 4188 4189 4191 4192 4193 4194 4196 4197 4198 4200 4201 4203
2 2 2 2 2 2 1 2 1 2 2 2 1 2 2 1
4206 4208 4209 4210 4212 4214 4215 4216 4217 4218 4220 4221 4225 4226 4228 4231
2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 1
4232 4233 4234 4235 4236 4238 4239 4240 4242 4243 4245 4246 4247 4252 4253 4255
1 2 2 2 2 2 1 1 1 2 2 2 1 2 2 2
4257 4258 4259 4260 4261 4263 4264 4265 4266 4267 4268 4269 4270 4272 4274 4275
2 2 2 2 2 1 2 1 2 2 2 2 1 1 2 2
4276 4278 4279 4281 4285 4286 4287 4288 4289 4290 4292 4293 4295 4296 4298 4299
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1
4300 4301 4302 4303 4305 4307 4309 4310 4311 4313 4314 4315 4316 4317 4318 4319
2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2
4320 4321 4322 4326 4328 4330 4331 4332 4334 4336 4337 4340 4341 4345 4346 4348
2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2
4349 4350 4351 4352 4354 4355 4357 4358 4359 4360 4361 4362 4363 4364 4365 4366
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
4367 4368 4369 4370 4372 4373 4375 4377 4379 4380 4381 4382 4383 4384 4385 4386
2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 2
4389 4390 4392 4393 4395 4396 4398 4399 4400 4402 4403 4404 4406 4408 4409 4411
2 2 2 2 2 2 1 2 2 2 1 2 2 2 2 2
4412 4414 4415 4417 4418 4419 4420 4421 4425 4426 4427 4428 4429 4432 4433 4434
2 2 2 2 2 2 2 2 1 2 1 1 2 2 2 2
4436 4437 4438 4440 4441 4443 4444 4445 4446 4447 4449 4450 4451 4452 4454 4458
2 1 2 2 2 1 2 1 2 2 2 2 2 2 2 2
4459 4460 4462 4464 4465 4466 4467 4468 4469 4471 4472 4474 4475 4476 4477 4480
2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2
4482 4483 4484 4485 4486 4487 4489 4491 4492 4493 4494 4496 4500 4501 4502 4503
2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
4504 4506 4507 4509 4510 4511 4513 4515 4516 4517 4518 4519 4520 4524 4525 4526
2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2
4528 4530 4531 4533 4534 4535 4536 4537 4541 4543 4545 4546 4547 4550 4551 4553
2 2 2 2 1 1 2 2 2 2 2 2 1 1 1 2
4557 4558 4559 4561 4562 4565 4566 4567 4568 4569 4570 4571 4572 4574 4575 4576
2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2
4577 4578 4579 4582 4583 4585 4587 4588 4589 4590 4591 4593 4594 4595 4596 4597
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
4598 4599 4601 4602 4604 4605 4606 4607 4608 4610 4611 4612 4613 4615 4616 4617
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
4619 4620 4622 4623 4628 4629 4630 4631 4632 4633 4634 4635 4636 4637 4638 4640
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
4642 4643 4645 4646 4647 4651 4652 4653 4654 4656 4657 4658 4659 4661 4663 4664
1 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2
4666 4668 4669 4671 4672 4673 4675 4676 4677 4679 4680 4681 4682 4683 4684 4685
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
4686 4687 4688 4689 4690 4691 4692 4696 4698 4702 4703 4705 4706 4707 4708 4709
1 1 2 2 2 2 2 2 2 1 1 2 2 1 1 2
4711 4712 4713 4714 4717 4718 4719 4720 4721 4723 4724 4726 4728 4729 4730 4731
2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
4732 4733 4734 4735 4736 4737 4738 4739 4740 4742 4745 4746 4749 4750 4751 4752
2 2 2 2 2 1 2 2 2 2 2 1 2 2 2 2
4754 4755 4756 4757 4758 4761 4762 4763 4764 4765 4766 4770 4771 4772 4773 4775
2 2 2 2 1 1 2 2 2 2 1 2 2 2 1 2
4777 4779 4780 4781 4782 4783 4784 4785 4786 4787 4788 4791 4792 4793 4795 4797
2 2 2 2 1 2 2 2 2 2 2 2 2 1 2 1
4798 4799 4800 4801 4802 4803 4804 4805 4806 4809 4811 4812 4813 4814 4816 4817
2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2
4818 4819 4821 4823 4824 4825 4826 4827 4828 4829 4830 4831 4832 4834 4835 4838
2 2 2 2 1 2 2 2 2 2 2 1 2 1 2 2
4839 4840 4844 4845 4847 4849 4850 4851 4853 4854 4855 4857 4858 4859 4860 4862
2 2 1 2 2 2 2 2 1 2 2 2 2 2 2 2
4863 4864 4865 4868 4869 4870 4872 4873 4874 4876 4878 4881 4882 4883 4884 4885
1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2
4886 4889 4890 4892 4894 4895 4901 4902 4904 4906 4907 4908 4909 4910 4912 4913
2 1 2 2 2 2 2 1 2 2 2 1 2 2 2 2
4914 4917 4918 4920 4921 4923 4924 4925 4927 4928 4929 4930 4931 4932 4934 4935
2 2 1 1 2 2 2 2 2 1 2 2 2 2 2 2
4936 4938 4940 4941 4945 4947 4948 4949 4951 4952 4954 4955 4956 4957 4959 4960
2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2
4961 4964 4966 4967 4969 4971 4972 4973 4975 4980 4981 4982 4983 4984 4986 4987
2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
4989 4990 4991 4993 4995 4998 4999 5000 5001 5002 5003 5005 5007 5008 5009 5011
2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2
5012 5013 5014 5017 5018 5019 5020 5021 5023 5024 5027 5028 5029 5030 5033 5034
2 2 2 2 2 2 2 2 1 1 1 2 2 1 1 2
5035 5036 5037 5038 5041 5043 5045 5047 5048 5049 5050 5051 5053 5054 5055 5057
1 1 2 1 1 2 1 2 1 2 2 1 2 2 2 2
5058 5061 5062 5063 5064 5065 5067 5068 5069 5070 5073 5074 5076 5077 5079 5080
1 2 2 1 1 2 2 2 2 1 2 2 2 2 2 2
5081 5084 5085 5089 5090 5095 5097 5098 5101 5102 5103 5105 5106 5108 5109 5110
2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2
5111 5112 5113 5114 5115 5116 5118 5120 5122 5123 5124 5125 5127 5128 5129 5130
2 1 2 2 2 1 1 1 2 2 2 2 2 2 2 2
5131 5132 5133 5135 5138 5140 5142 5143 5144 5147 5149 5151 5152 5153 5154 5156
2 1 2 2 2 2 1 2 2 1 2 2 2 2 2 2
5157 5158 5159 5160 5161 5162 5165 5166 5167 5169 5170 5171 5175 5177 5178 5179
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
5180 5183 5184 5185 5186 5188 5189 5190 5191 5192 5193 5194 5195 5196 5199 5200
2 2 2 2 2 2 2 2 2 1 2 2 1 2 2 1
5202 5203 5204 5205 5206 5207 5208 5209 5211 5213 5215 5216 5217 5218 5219 5222
2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2
5224 5226 5228 5231 5234 5236 5237 5239 5240 5241 5243 5244 5245 5246 5248 5249
2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2
5251 5253 5255 5256 5257 5258 5259 5262 5265 5266 5269 5270 5272 5273 5274 5275
2 2 2 2 2 2 1 2 2 1 2 2 2 1 2 2
5276 5277 5279 5280 5282 5283 5284 5285 5286 5287 5288 5289 5290 5291 5292 5293
1 2 2 2 1 2 2 1 2 2 1 2 2 2 2 2
5294 5295 5296 5297 5298 5299 5301 5302 5309 5311 5312 5313 5314 5315 5317 5319
2 2 1 2 2 2 1 1 1 2 2 2 2 2 2 2
5321 5323 5326 5327 5328 5329 5330 5334 5335 5336 5337 5339 5341 5342 5343 5344
2 2 1 2 1 2 2 2 2 2 2 2 2 2 2 2
5345 5346 5347 5351 5352 5353 5354 5355 5357 5359 5360 5361 5362 5363 5365 5366
2 1 2 2 2 2 2 1 2 1 1 1 1 2 2 2
5367 5370 5371 5374 5375 5376 5377 5379 5382 5385 5386 5387 5388 5390 5391 5393
1 2 2 2 2 1 2 2 2 1 2 2 2 2 2 2
5395 5396 5397 5398 5399 5400 5401 5402 5403 5404 5405 5406 5407 5408 5409 5410
2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2
5411 5412 5413 5414 5416 5418 5419 5420 5421 5422 5424 5425 5426 5427 5428 5429
2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2
5431 5432 5434 5437 5438 5439 5440 5441 5442 5443 5444 5445 5447 5450 5452 5454
2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2
5455 5457 5459 5460 5461 5466 5468 5469 5470 5471 5472 5474 5475 5476 5477 5478
1 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2
5480 5481 5485 5486 5489 5490 5491 5494 5495 5496 5498 5499 5500 5502 5506 5507
2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2
5508 5509 5510 5511 5512 5513 5514 5515 5516 5517 5518 5521 5522 5523 5525 5526
2 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2
5528 5529 5530 5531 5533 5534 5536 5537 5539 5540 5541 5543 5544 5545 5547 5550
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
5551 5552 5554 5555 5556 5558 5559 5561 5562 5563 5564 5565 5566 5567 5569 5571
2 2 2 2 1 2 2 2 2 1 2 2 1 1 2 2
5572 5573 5574 5575 5576 5577 5578 5580 5582 5583 5584 5585 5587 5588 5590 5591
1 2 2 1 2 2 2 1 2 2 1 1 1 2 2 2
5592 5593 5594 5596 5597 5598 5599 5601 5602 5603 5604 5606 5607 5609 5610 5612
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
5614 5616 5617 5618 5620 5621 5622 5625 5627 5628 5629 5631 5633 5634 5637 5638
2 1 2 2 1 2 2 2 2 2 2 2 2 1 1 2
5640 5642 5644 5645 5647 5649 5651 5652 5655 5656 5658 5659 5660 5661 5662 5663
2 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2
5664 5665 5666 5668 5669 5670 5671 5672 5673 5674 5675 5677 5678 5679 5681 5682
2 2 2 2 2 2 2 1 2 1 2 2 2 2 1 2
5683 5684 5686 5687 5688 5689 5690 5695 5696 5697 5698 5699 5701 5702 5706 5707
2 2 2 2 2 1 2 2 2 1 2 2 2 1 2 2
5708 5709 5710 5711 5712 5714 5718 5721 5722 5723 5724 5726 5727 5728 5733 5734
2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2
5735 5736 5738 5741 5742 5743 5745 5748 5749 5750 5753 5755 5756 5758 5759 5760
2 2 2 2 2 2 2 2 1 2 2 2 2 2 1 2
5763 5764 5766 5767 5768 5769 5770 5771 5774 5775 5776 5777 5778 5779 5781 5782
2 1 1 2 2 2 2 2 2 1 2 2 2 2 2 2
5784 5785 5788 5789 5790 5792 5793 5794 5796 5797 5798 5799 5800 5802 5803 5805
2 1 1 2 1 1 2 2 2 2 2 2 2 2 1 1
5806 5807 5810 5813 5821 5822 5823 5824 5825 5827 5830 5831 5834 5835 5837 5838
1 1 1 2 2 2 2 2 2 2 2 1 2 1 2 2
5842 5844 5845 5846 5847 5848 5849 5850 5851 5853 5855 5861 5862 5863 5864 5865
2 2 2 2 2 1 2 2 2 2 2 2 2 1 2 2
5866 5867 5870 5871 5873 5874 5875 5876 5878 5879 5880 5882 5883 5884 5885 5886
2 2 2 2 2 2 2 1 1 1 2 1 2 1 2 2
5889 5891 5892 5893 5894 5895 5896 5897 5898 5899 5900 5901 5903 5904 5905 5907
1 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2
5908 5909 5911 5912 5914 5915 5916 5917 5918 5920 5921 5923 5924 5926 5927 5929
2 2 2 1 1 2 2 2 2 2 2 2 1 2 2 2
5930 5931 5932 5933 5934 5935 5937 5938 5940 5942 5945 5946 5947 5949 5950 5951
2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2
5953 5954 5955 5956 5957 5958 5959 5960 5961 5962 5963 5968 5971 5972 5973 5974
2 2 2 2 1 2 2 2 2 2 2 2 1 2 2 1
5976 5978 5979 5980 5981 5982 5983 5984 5985 5986 5989 5990 5991 5992 5995 5997
2 2 2 2 1 2 1 2 2 2 2 2 2 1 2 2
5998 5999 6000 6001 6002 6003 6005 6008 6009 6010 6012 6014 6015 6017 6019 6021
2 2 2 2 2 1 2 2 1 2 2 2 1 2 1 2
6023 6024 6025 6027 6028 6029 6030 6033 6034 6035 6036 6037 6041 6043 6044 6045
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6049 6050 6051 6052 6054 6060 6061 6062 6063 6064 6065 6066 6067 6068 6069 6072
2 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2
6073 6074 6075 6076 6077 6078 6081 6082 6083 6085 6086 6092 6093 6094 6095 6096
2 1 2 1 2 2 2 2 2 2 2 1 2 2 2 2
6098 6101 6102 6104 6105 6106 6107 6108 6109 6111 6112 6114 6116 6118 6120 6122
2 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2
6123 6124 6127 6129 6130 6134 6135 6136 6138 6139 6140 6141 6142 6144 6147 6148
2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2
6150 6152 6153 6154 6156 6157 6158 6159 6162 6163 6165 6167 6168 6170 6171 6172
2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2
6175 6177 6179 6180 6182 6184 6185 6186 6187 6188 6189 6191 6193 6196 6200 6202
1 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2
6203 6204 6206 6208 6211 6212 6213 6214 6216 6217 6218 6219 6220 6221 6222 6224
2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2
6225 6228 6229 6230 6231 6232 6234 6237 6239 6240 6242 6243 6246 6247 6250 6251
2 2 2 1 1 2 2 2 2 2 2 2 1 2 2 2
6252 6253 6254 6255 6260 6261 6262 6263 6264 6268 6270 6271 6272 6274 6276 6277
2 2 2 2 2 2 2 2 2 2 1 2 1 2 2 1
6278 6279 6280 6282 6283 6284 6285 6286 6287 6289 6290 6292 6294 6296 6297 6298
2 1 2 1 2 1 2 2 2 2 1 1 2 2 2 2
6299 6300 6302 6303 6304 6305 6306 6307 6309 6311 6312 6313 6315 6317 6319 6321
2 2 2 2 1 2 2 1 2 2 2 1 2 2 1 2
6322 6323 6324 6325 6327 6328 6329 6330 6333 6334 6335 6338 6341 6343 6345 6346
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6347 6349 6350 6351 6352 6354 6358 6359 6360 6361 6362 6363 6364 6365 6367 6369
2 2 2 2 2 1 2 1 2 2 1 2 2 2 1 2
6370 6371 6372 6374 6376 6377 6378 6379 6380 6382 6383 6384 6385 6386 6387 6388
1 2 1 2 2 2 2 2 2 2 2 2 2 1 2 2
6389 6392 6394 6395 6396 6397 6399 6402 6403 6404 6405 6406 6407 6408 6411 6413
1 1 1 2 2 1 1 2 2 2 2 2 2 2 2 2
6414 6417 6418 6419 6420 6422 6423 6424 6425 6426 6428 6429 6430 6431 6432 6433
2 1 1 2 2 2 1 2 2 1 2 2 2 2 2 2
6434 6436 6438 6439 6440 6441 6444 6445 6446 6448 6451 6452 6453 6456 6457 6458
1 2 2 2 2 2 2 1 2 2 2 1 2 2 2 1
6461 6462 6463 6466 6467 6469 6470 6471 6472 6473 6474 6475 6476 6477 6479 6484
2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
6485 6486 6488 6489 6490 6491 6492 6493 6494 6495 6496 6497 6498 6499 6500 6502
1 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
6504 6506 6507 6510 6511 6513 6514 6516 6519 6520 6526 6527 6530 6531 6533 6534
1 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2
6535 6536 6537 6538 6539 6540 6541 6543 6544 6545 6546 6548 6550 6551 6554 6555
2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2
6556 6557 6558 6560 6562 6564 6565 6566 6567 6568 6570 6571 6572 6575 6578 6579
2 2 2 1 1 1 2 2 2 1 2 2 2 2 2 2
6580 6582 6583 6584 6585 6587 6590 6591 6592 6593 6595 6596 6598 6599 6600 6602
2 2 2 2 2 2 2 2 2 2 1 2 1 2 2 2
6603 6604 6605 6607 6608 6609 6610 6611 6612 6614 6616 6617 6618 6620 6621 6622
2 2 2 2 2 2 2 1 1 2 2 2 2 1 2 2
6624 6625 6626 6627 6629 6630 6631 6632 6635 6636 6637 6639 6643 6644 6647 6648
2 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2
6650 6651 6653 6656 6657 6658 6659 6660 6662 6664 6667 6668 6671 6672 6675 6677
1 2 2 2 2 1 2 1 1 2 2 2 2 2 2 2
6678 6680 6681 6683 6684 6685 6687 6688 6689 6691 6692 6693 6694 6695 6697 6699
2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2
6701 6703 6704 6706 6707 6709 6711 6713 6714 6715 6717 6719 6721 6723 6724 6725
1 2 1 2 2 2 2 2 1 2 2 2 2 2 2 2
6726 6731 6732 6733 6735 6736 6738 6740 6743 6744 6745 6746 6748 6749 6750 6751
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6752 6753 6754 6755 6757 6758 6759 6761 6763 6764 6767 6768 6771 6773 6774 6777
2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 2
6778 6779 6780 6781 6782 6783 6784 6785 6786 6787 6788 6789 6793 6794 6796 6798
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1
6799 6800 6802 6803 6805 6806 6807 6811 6814 6818 6819 6820 6822 6823 6825 6826
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6827 6828 6829 6832 6835 6837 6838 6839 6840 6842 6845 6846 6847 6848 6850 6851
2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 1
6852 6853 6854 6855 6856 6857 6858 6860 6861 6864 6866 6867 6868 6869 6870 6871
1 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2
6872 6873 6874 6875 6876 6877 6878 6879 6880 6881 6882 6883 6884 6885 6887 6888
2 2 2 2 2 1 2 2 2 1 2 2 2 2 2 2
6889 6890 6891 6893 6894 6895 6897 6899 6901 6904 6905 6906 6907 6909 6910 6912
2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6913 6914 6915 6916 6917 6918 6919 6920 6922 6923 6924 6925 6926 6927 6928 6931
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6933 6934 6935 6938 6939 6940 6941 6942 6944 6945 6946 6948 6949 6951 6952 6954
2 2 2 2 2 2 2 2 2 1 2 1 2 2 2 2
6955 6956 6958 6962 6967 6969 6971 6973 6974 6977 6979 6980 6981 6982 6984 6985
2 1 2 1 2 2 2 1 2 2 2 2 2 1 2 2
6986 6990 6991 6993 6994 6997 6998 6999 7000 7001 7002 7004 7005 7007 7008 7012
2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1
7013 7014 7015 7017 7019 7020 7022 7023 7024 7027 7028 7029 7030 7031 7032 7033
2 2 1 2 2 1 2 2 2 2 2 2 1 2 2 2
7034 7036 7037 7040 7041 7042 7043 7045 7046 7047 7048 7049 7050 7051 7052 7053
2 2 2 2 2 2 2 2 2 1 2 2 2 1 2 2
7056 7059 7060 7061 7063 7064 7066 7067 7068 7069 7070 7071 7072 7073 7075 7076
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
7077 7078 7080 7082 7083 7084 7085 7088 7089 7092 7093 7095 7096 7097 7098 7099
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
7101 7102 7103 7104 7105 7106 7107 7108 7111 7114 7115 7116 7117 7118 7119 7120
2 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2
7121 7122 7123 7125 7126 7127 7129 7130 7131 7132 7135 7136 7137 7138 7139 7140
2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 2
7141 7142 7143 7144 7145 7147 7148 7151 7152 7153 7154 7155 7157 7158 7160 7161
2 1 2 1 1 2 2 2 2 2 2 2 2 1 2 2
7162 7163 7166 7168 7169 7172 7173 7174 7176 7177 7179 7181 7182 7183 7184 7185
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
7188 7189 7192 7193 7194 7199 7200 7201 7205 7206 7207 7208 7209 7211 7213 7214
2 2 2 1 1 2 2 2 1 2 2 2 2 2 2 2
7216 7218 7219 7220 7221 7223 7225 7226 7227 7230 7231 7232 7234 7235 7236 7237
1 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2
7240 7241 7242 7243 7244 7245 7246 7248 7250 7251 7252 7254 7256 7257 7258 7259
1 2 1 2 2 2 2 2 2 2 1 2 2 1 2 2
7260 7261 7262 7265 7266 7267 7268 7269 7270 7271 7272 7273 7274 7276 7277 7280
2 2 2 1 2 2 1 1 1 2 2 2 2 2 2 2
7281 7285 7286 7287 7289 7290 7291 7293 7294 7295 7296 7297 7299 7302 7306 7308
2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2
7309 7310 7311 7313 7314 7315 7316 7318 7319 7320 7321 7322 7324 7327 7330 7332
2 2 2 1 2 2 1 2 2 2 2 2 2 1 1 2
7336 7337 7338 7339 7340 7341 7342 7343 7345 7346 7347 7348 7350 7353 7354 7356
2 2 2 2 1 2 2 2 2 2 2 2 1 2 2 2
7360 7361 7363 7365 7367 7368 7369 7370 7371 7372 7373 7374 7376 7377 7379 7384
2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2
7385 7386 7388 7389 7393 7394 7395 7396 7397 7398 7400 7403 7404 7405 7406 7407
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
7410 7415 7416 7417 7421 7422 7423 7424 7428 7429 7430 7432 7434 7435 7436 7437
2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2
7438 7439 7441 7444 7447 7448 7449 7450 7451 7452 7453 7454 7455 7456 7457 7459
2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2
7460 7462 7464 7466 7467 7468 7469 7470 7472 7473 7474 7475 7476 7477 7478 7479
1 2 1 1 2 2 2 1 2 2 2 2 2 2 2 2
7481 7482 7484 7485 7487 7488 7493 7497 7498 7505 7506 7507 7508 7509 7510 7511
2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2
7512 7513 7514 7515 7517 7518 7519 7521 7522 7523 7525 7526 7527 7528 7529 7531
2 2 2 1 2 1 2 2 2 2 2 2 2 2 2 2
7534 7540 7541 7542 7543 7546 7549 7550 7551 7552 7553 7555 7556 7557 7558 7559
1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2
7560 7561 7562 7563 7567 7568 7570 7573 7574 7575 7576 7578 7580 7582 7584 7586
1 1 1 2 2 2 2 2 2 2 2 2 2 1 2 2
7587 7588 7590 7591 7592 7594 7595 7596 7597 7598 7600 7601 7603 7605 7606 7608
2 1 2 1 2 2 2 2 2 2 2 2 1 2 2 2
7609 7611 7612 7613 7614 7615 7616 7617 7619 7620 7623 7625 7627 7628 7629 7630
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
7631 7632 7633 7634 7635 7637 7638 7641 7642 7643 7645 7646 7648 7649 7650 7651
2 2 2 1 2 2 1 2 2 2 1 1 2 2 2 2
7652 7653 7656 7657 7658 7659 7660 7661 7663 7664 7665 7666 7669 7670 7671 7672
2 2 2 2 2 2 2 2 2 2 2 1 2 2 1 2
7673 7674 7675 7677 7678 7679 7680 7681 7684 7685 7686 7687 7689 7690 7692 7693
2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2
7694 7695 7697 7699 7700 7701 7702 7703 7705 7706 7708 7709 7711 7712 7713 7714
2 2 1 2 2 2 2 2 2 1 2 1 2 2 2 1
7718 7719 7720 7721 7722 7724 7726 7728 7729 7732 7733 7734 7737 7738 7739 7741
2 2 2 1 2 1 1 1 1 2 2 2 2 2 2 2
7742 7743 7744 7745 7746 7747 7749 7750 7751 7752 7753 7754 7758 7764 7766 7769
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
7770 7771 7772 7773 7776 7777 7778 7779 7782 7783 7787 7788 7791 7792 7794 7795
2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2
7796 7798 7801 7802 7803 7804 7805 7806 7807 7808 7809 7810 7812 7814 7815 7818
2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2
7819 7820 7821 7823 7824 7825 7826 7827 7828 7829 7830 7832 7833 7834 7836 7837
2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2
7838 7840 7842 7843 7844 7845 7846 7847 7849 7851 7853 7854 7855 7856 7857 7860
2 2 2 2 1 2 2 2 2 2 2 2 1 1 2 2
7861 7863 7864 7866 7867 7869 7871 7872 7874 7876 7877 7878 7879 7880 7881 7882
2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
7883 7884 7885 7886 7887 7888 7889 7890 7891 7892 7894 7895 7896 7898 7899 7900
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
7903 7905 7906 7907 7908 7909 7910 7911 7913 7914 7917 7919 7920 7921 7922 7923
2 1 2 2 2 2 2 2 2 2 2 2 1 2 2 2
7925 7926 7929 7930 7931 7932 7935 7936 7937 7938 7943 7945 7946 7949 7950 7951
1 2 2 2 1 2 2 1 1 1 2 2 2 2 1 1
7953 7954 7956 7957 7958 7959 7962 7963 7964 7965 7966 7968 7969 7971 7972 7973
2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2
7974 7976 7977 7978 7979 7981 7982 7983 7985 7989 7990 7991 7993 7994 7996 7999
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
8000 8001 8002 8004 8005 8006 8008 8009 8010 8011 8013 8014 8015 8016 8017 8018
2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2
8019 8020 8022 8023 8025 8026 8027 8028 8030 8031 8032 8033 8034 8035 8036 8038
2 2 1 2 1 2 2 2 2 1 2 2 1 1 2 2
8039 8040 8042 8043 8044 8046 8048 8049 8050 8051 8053 8055 8056 8057 8058 8059
2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 1
8061 8062 8063 8064 8066 8068 8069 8070 8073 8074 8075 8076 8077 8078 8079 8080
2 2 2 2 2 2 2 2 2 2 2 1 1 1 2 2
8083 8084 8085 8086 8087 8088 8089 8090 8093 8094 8097 8100 8101 8102 8103 8104
2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2
8105 8106 8107 8109 8110 8111 8112 8113 8115 8117 8118 8122 8124 8125 8126 8127
2 2 2 2 2 2 1 2 1 2 2 2 2 2 2 2
8128 8130 8131 8133 8134 8135 8136 8138 8139 8140 8142 8143 8147 8148 8150 8151
2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1
8152 8153 8155 8156 8157 8159 8160 8161 8163 8164 8166 8167 8170 8171 8172 8173
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
8174 8175 8177 8179 8180 8181 8182 8183 8184 8185 8186 8187 8188 8189 8190 8191
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
8194 8195 8196 8197 8199 8200 8202 8203 8204 8206 8207 8208 8210 8211 8212 8213
2 2 2 1 2 2 2 1 2 2 1 2 2 2 2 2
8214 8215 8216 8217 8218 8219 8221 8222 8223 8224 8225 8226 8230 8231 8232 8234
2 2 2 2 2 1 2 2 1 1 2 2 2 1 2 2
8236 8237 8239 8240 8241 8242 8244 8245 8246 8248 8249 8250 8253 8254 8255 8256
2 1 1 1 2 1 2 2 1 2 2 1 2 2 1 2
8257 8259 8260 8262 8263 8267 8268 8269 8270 8271 8273 8274 8275 8277 8278 8279
2 2 2 2 2 2 1 2 2 2 1 2 2 2 2 2
8280 8281 8283 8284 8285 8286 8287 8288 8289 8291 8292 8293 8294 8295 8296 8297
2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 1
8298 8299 8300 8303 8306 8308 8311 8314 8317 8318 8319 8320 8321 8322 8323 8325
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
8326 8327 8329 8330 8331 8333 8334 8336 8337 8338 8339 8341 8342 8347 8349 8350
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
8351 8352 8353 8354 8358 8360 8361 8363 8364 8365 8366 8368 8369 8370 8371 8372
2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
8373 8375 8376 8377 8378 8379 8380 8382 8383 8384 8387 8388 8390 8392 8393 8394
2 2 2 2 1 1 2 2 1 2 2 1 1 2 2 1
8395 8396 8399 8400 8401 8402 8405 8406 8408 8409 8410 8412 8413 8414 8415 8416
2 2 2 2 2 2 2 2 1 1 1 2 2 2 2 2
8418 8419 8421 8422 8423 8424 8425 8426 8428 8429 8430 8431 8434 8435 8436 8437
2 2 2 2 1 2 2 2 1 1 2 2 2 1 2 2
8440 8442 8443 8444 8445 8446 8450 8452 8454 8455 8456 8458 8459 8463 8464 8465
2 1 2 2 2 2 2 2 1 2 2 1 2 2 2 1
8466 8467 8468 8469 8470 8472 8474 8476 8477 8478 8479 8481 8483 8487 8488 8489
1 2 2 2 1 2 2 2 2 2 2 1 2 1 1 1
8490 8491 8492 8493 8495 8496 8497 8500 8501 8503 8504 8506 8507 8508 8511 8514
2 1 2 2 2 2 2 1 2 2 2 2 2 2 2 2
8515 8516 8517 8518 8519 8520 8521 8522 8525 8526 8527 8528 8529 8532 8534 8536
1 1 2 2 2 2 2 2 2 2 2 1 2 2 2 2
8537 8538 8541 8542 8543 8545 8546 8547 8548 8549 8550 8551 8553 8555 8556 8557
2 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2
8560 8561 8562 8563 8564 8565 8569 8570 8571 8572 8573 8574 8575 8577 8578 8579
2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 1
8583 8584 8588 8589 8591 8592 8594 8595 8598 8600 8601 8602 8603 8605 8607 8608
2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2
8609 8610 8611 8612 8614 8615 8617 8620 8621 8622 8623 8625 8626 8627 8629 8631
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
8632 8633 8635 8636 8643 8645 8646 8647 8650 8653 8654 8655 8656 8657 8658 8662
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
8664 8665 8666 8668 8669 8670 8672 8673 8674 8675 8676 8677 8678 8680 8681 8687
1 2 2 2 2 1 2 2 1 2 2 2 2 2 2 1
8689 8691 8692 8694 8695 8697 8698 8703 8704 8705 8707 8708 8710 8711 8715 8718
1 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2
8719 8722 8723 8725 8726 8728 8729 8731 8732 8733 8734 8735 8737 8738 8740 8743
2 2 2 2 1 2 2 2 1 2 2 2 2 2 2 2
8744 8745 8746 8748 8749 8751 8753 8754 8755 8756 8757 8758 8760 8761 8763 8764
2 2 2 2 2 2 1 1 1 2 2 2 2 2 1 2
8765 8766 8767 8768 8769 8770 8772 8775 8776 8777 8779 8780 8781 8782 8783 8784
1 2 2 1 1 2 2 2 2 2 2 2 1 2 1 2
8786 8787 8788 8789 8790 8791 8793 8795 8796 8799 8800 8801 8802 8803 8804 8807
2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 1
8808 8809 8810 8812 8814 8815 8816 8817 8818 8819 8821 8822 8823 8824 8826 8827
2 2 2 2 2 2 2 1 2 2 2 1 2 2 2 2
8828 8829 8831 8832 8835 8839 8840 8842 8845 8846 8849 8850 8853 8854 8855 8856
2 2 2 2 2 2 1 2 2 2 1 2 2 2 2 2
8857 8858 8861 8862 8863 8868 8869 8871 8872 8873 8874 8875 8876 8878 8879 8880
2 2 2 2 2 2 2 2 1 2 2 2 2 2 1 1
8881 8883 8884 8885 8886 8889 8890 8893 8894 8897 8899 8900 8903 8904 8906 8908
2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2
8909 8912 8913 8914 8916 8918 8919 8920 8922 8923 8924 8925 8926 8927 8928 8929
2 2 2 1 2 1 2 1 2 2 2 2 2 2 1 2
8931 8933 8936 8938 8939 8942 8944 8945 8946 8947 8949 8950 8951 8954 8955 8957
2 2 1 2 1 2 2 2 2 2 2 2 1 2 2 2
8958 8960 8961 8962 8963 8964 8965
2 2 2 2 2 2 2
Within cluster sum of squares by cluster:
[1] 24349805 37653165
(between_SS / total_SS = 31.6 %)
Available components:
[1] "cluster" "centers" "totss" "withinss" "tot.withinss"
[6] "betweenss" "size" "iter" "ifault" table(df$fibroscan_steatosis, df.kmeans$cluster)
1 2
Cases 598 1611
Controls 397 3513centers <- as.data.frame(df.kmeans$centers)
plot8 <- ggplot(data = df) +
geom_point(aes(body_bmi, ha1c,
color = factor(df.kmeans$cluster))) +
geom_point(data = centers, aes(body_bmi, ha1c),
color = "purple", size = 2)
plot8
10 Supervised machine learning using Random Forest Model to assess most important factors/GINI in Cirrhosis
For this we will have to convert the cases to 1 and controls to 0 as the “truth” argument of the predictor variable regonizes “Cases” and “Controls” best
#We will convert 1-> Cases and 0-> Controls
#Steatosis
df<- df |>
mutate(fibroscan_cirrhosis = ifelse(fibroscan_cirrhosis == 1, "Cases", "Controls"))
table(df$fibroscan_cirrhosis)
Cases Controls
109 6010 df$fibroscan_cirrhosis <- as.factor(df$fibroscan_cirrhosis)ggbetweenstats(
data = df,
x = fibroscan_cirrhosis,
y = body_bmi,
title = "Cirrhosis vs BMI ")
#Random forest model
rf_cls_spec <-
rand_forest(trees = 1000, min_n = 5) |>
set_engine("randomForest", importance = TRUE) |>
set_mode("classification")
rf_cls_specRandom Forest Model Specification (classification)
Main Arguments:
trees = 1000
min_n = 5
Engine-Specific Arguments:
importance = TRUE
Computational engine: randomForest rf_cls_fit_cirrhosis <- rf_cls_spec |>
fit(fibroscan_cirrhosis ~ alt + alb + alp + ast + urea + cr + ggt + ldh + na + tbil + chol + tg + etoh + ha1c + insurance_covered + demo_gender + demo_age + demo_race + demo_education + body_bmi + hcab + hbcore_positive + hcrna, data = df)
rf_cls_fit_cirrhosisparsnip model object
Call:
randomForest(x = maybe_data_frame(x), y = y, ntree = ~1000, nodesize = min_rows(~5, x), importance = ~TRUE)
Type of random forest: classification
Number of trees: 1000
No. of variables tried at each split: 4
OOB estimate of error rate: 1.83%
Confusion matrix:
Cases Controls class.error
Cases 1 108 0.9908256881
Controls 4 6006 0.0006655574#for importance scores
rf_cls_fit_cirrhosis |>
extract_fit_engine() |>
importance() Cases Controls MeanDecreaseAccuracy MeanDecreaseGini
alt -0.71229187 14.59273872 15.1872964 7.9252118
alb 12.46482099 14.79223333 17.4390842 8.4356280
alp 12.42697700 3.38075249 7.0562020 11.9331362
ast 12.50653795 9.80399117 11.5730609 9.2186021
urea -1.18788449 9.85177544 9.5706653 7.2163847
cr -0.31735998 13.74012774 13.8680114 8.0419054
ggt 14.81646114 4.88792309 8.6873163 10.8721959
ldh 5.11625436 5.71388665 6.9390205 11.5600712
na 0.91759659 0.01492991 0.2285551 5.4307804
tbil 10.63420464 9.13289595 11.9000997 7.3117497
chol 3.01143224 2.86092983 3.4832066 9.3489920
tg -0.02223564 5.19290592 5.2128027 8.7317406
etoh 0.64118901 3.04003500 3.0569302 1.3726879
ha1c 6.82846786 4.69231049 6.0176098 7.7142665
insurance_covered -1.52438408 4.11098061 3.6749184 0.5940544
demo_gender 0.06454764 15.79365642 15.7310349 1.8535442
demo_age -1.86747759 13.09220004 12.9026842 6.0835902
demo_race -2.81088625 8.94113961 8.1466809 5.0023135
demo_education 0.34335619 3.01451244 3.0418969 4.6297653
body_bmi 32.73825081 18.91319483 26.0798979 23.1840585
hcab 7.26908226 4.69870874 6.7055249 2.1654800
hbcore_positive 0.94938186 -0.63337453 -0.3311197 0.6728959
hcrna 6.38721664 4.58208233 6.3579045 1.7945368#to plot MeanDecreaseGini
rf_cls_fit_cirrhosis |>
extract_fit_engine() |>
vip()
#save
rf.predicted.cirrhosis <- bind_cols(
truth = df$fibroscan_cirrhosis,
predict(rf_cls_fit_cirrhosis, df),
predict(rf_cls_fit_cirrhosis, df, type = "prob")
)
rf.predicted.cirrhosis# A tibble: 6,119 × 4
truth .pred_class .pred_Cases .pred_Controls
<fct> <fct> <dbl> <dbl>
1 Controls Controls 0.001 0.999
2 Controls Controls 0.001 0.999
3 Controls Controls 0.001 0.999
4 Controls Controls 0.005 0.995
5 Controls Controls 0.002 0.998
6 Controls Controls 0 1
7 Controls Controls 0.002 0.998
8 Controls Controls 0.015 0.985
9 Controls Controls 0.002 0.998
10 Cases Cases 0.507 0.493
# ℹ 6,109 more rows#RF plots
plot13 <- autoplot(roc_curve(rf.predicted.cirrhosis,
truth, .pred_Cases ))
plot13 
plot14 <- roc_auc(rf.predicted.cirrhosis,
truth, .pred_Cases )
plot14# A tibble: 1 × 3
.metric .estimator .estimate
<chr> <chr> <dbl>
1 roc_auc binary 1For obtaining 10-fold cross validation classification vectors for the model
set.seed(1234)
data.split <- initial_split(df,
strata = fibroscan_cirrhosis,
prop = 0.80)
data.split<Training/Testing/Total>
<4895/1224/6119>data.train <- training(data.split)
data.test <- testing(data.split)Training based on RF model
rf_cls_fit_train<- rf_cls_spec |>
fit(fibroscan_cirrhosis ~ ., data = data.train)
rf_cls_fit_trainparsnip model object
Call:
randomForest(x = maybe_data_frame(x), y = y, ntree = ~1000, nodesize = min_rows(~5, x), importance = ~TRUE)
Type of random forest: classification
Number of trees: 1000
No. of variables tried at each split: 5
OOB estimate of error rate: 1.74%
Confusion matrix:
Cases Controls class.error
Cases 1 82 0.9879518072
Controls 3 4809 0.0006234414Testing based on RF model
data.rf.pred.values.test <- bind_cols(
truth = data.test$fibroscan_cirrhosis,
predict(rf_cls_fit_train, data.test),
predict(rf_cls_fit_train, data.test, type = "prob")
)
data.rf.pred.values.test# A tibble: 1,224 × 4
truth .pred_class .pred_Cases .pred_Controls
<fct> <fct> <dbl> <dbl>
1 Controls Controls 0.004 0.996
2 Controls Controls 0.002 0.998
3 Controls Controls 0.014 0.986
4 Controls Controls 0.001 0.999
5 Controls Controls 0.004 0.996
6 Controls Controls 0 1
7 Controls Controls 0.002 0.998
8 Controls Controls 0 1
9 Controls Controls 0.016 0.984
10 Controls Controls 0.007 0.993
# ℹ 1,214 more rowsROC and AUC Curves
autoplot(roc_curve(data.rf.pred.values.test,
truth, .pred_Cases))
roc_auc(data.rf.pred.values.test,
truth, .pred_Cases)# A tibble: 1 × 3
.metric .estimator .estimate
<chr> <chr> <dbl>
1 roc_auc binary 0.84911 Unsupervised machine learning using Kmeans clustering in cirrhosis
set.seed(1234)
df.kmeans <- kmeans(df[ , 1:24], 2)
df.kmeansK-means clustering with 2 clusters of sizes 995, 5124
Cluster means:
alt alb alp ast urea cr ggt ldh
1 29.18392 4.084121 82.52462 24.49648 15.97990 0.9291658 50.20201 157.3598
2 21.16608 4.064637 76.09719 21.39617 14.70258 0.9015925 28.89325 158.0911
na tbil chol tg etoh ha1c hc_self_cpiqr
1 140.1518 0.4215075 209.5337 286.6874 1.827136 6.250854 33.63618
2 140.6899 0.4695160 181.1401 105.3134 1.859875 5.754313 37.62627
insurance_covered demo_gender demo_age demo_race demo_education body_bmi
1 1.20000 1.361809 52.31960 3.204020 3.437186 31.91015
2 1.16491 1.516784 50.13661 3.418033 3.659251 29.80289
hb_self_reported hc_self_reported hc_self_reported.1
1 2.006030 2.009045 2.009045
2 2.020101 2.011905 2.011905
Clustering vector:
1 2 3 4 5 8 10 11 13 14 15 18 19 20 21 23
2 2 2 2 2 2 2 1 2 1 2 2 2 2 2 2
30 31 34 35 36 37 38 40 42 43 44 45 47 48 49 50
2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2
51 53 54 55 56 57 58 61 62 63 64 65 66 67 68 69
2 2 2 2 2 2 1 2 2 2 2 1 2 2 2 1
70 71 72 73 74 76 78 79 80 82 84 86 87 89 91 92
2 2 2 2 2 2 1 2 2 1 2 2 2 2 2 1
93 95 96 97 98 99 103 104 105 106 107 109 110 112 113 116
2 1 2 2 2 2 2 2 1 2 1 1 2 1 2 1
117 118 119 121 122 123 124 125 126 127 129 131 132 133 134 136
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
137 139 141 143 144 145 146 147 148 149 150 151 152 155 156 157
2 2 2 2 2 1 2 1 2 2 1 2 2 2 2 2
158 159 162 163 164 165 166 167 169 171 173 174 178 179 180 181
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
182 183 184 185 186 189 190 191 192 193 194 195 196 198 200 201
2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2
203 206 207 209 210 211 213 215 216 217 219 220 222 225 226 228
2 2 2 1 2 2 2 2 2 2 2 2 2 2 1 2
229 230 231 233 235 237 238 239 240 241 243 244 245 248 249 250
2 2 2 1 1 2 2 1 2 2 2 2 2 2 1 1
252 253 254 257 259 260 261 262 263 264 266 267 268 269 270 272
2 2 2 2 2 2 2 2 2 1 2 1 2 2 1 2
273 275 276 277 279 280 281 283 284 285 287 288 289 290 293 294
2 1 2 2 2 2 2 2 2 1 2 2 2 1 2 2
295 300 301 303 305 306 308 309 310 311 312 314 315 316 320 322
1 1 2 2 2 2 1 2 2 2 2 2 2 1 2 2
324 325 326 327 328 329 330 331 333 336 337 338 339 342 343 344
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
345 346 348 349 350 351 352 355 357 359 360 361 363 364 365 367
1 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2
368 372 374 375 376 377 380 382 383 384 387 388 389 390 392 395
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
396 397 399 400 401 402 403 406 408 409 410 411 412 413 414 415
2 2 2 2 2 2 2 1 2 1 2 1 2 2 2 2
416 417 418 419 420 421 422 424 425 426 427 428 429 430 431 435
1 2 2 2 2 1 2 1 2 2 2 2 2 2 2 2
436 437 438 441 443 444 445 446 447 449 450 452 455 457 458 459
2 1 1 2 2 1 2 2 2 2 2 2 2 1 2 2
460 461 462 463 464 465 467 468 470 472 473 474 475 476 477 478
1 2 2 1 1 2 2 1 2 2 2 2 2 1 2 2
479 480 481 482 483 484 485 486 487 488 489 490 491 495 497 498
1 2 1 2 2 2 1 2 2 1 2 2 2 2 2 2
500 501 503 505 506 507 508 511 512 513 514 516 517 518 519 524
2 2 1 2 2 2 2 2 2 2 2 2 2 2 1 2
526 527 528 531 532 533 534 535 536 538 539 540 541 542 544 546
2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2
548 553 557 558 559 561 562 563 564 565 566 567 568 569 570 571
2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2
572 573 574 575 576 578 579 580 581 583 585 586 587 589 590 591
1 2 2 2 2 2 1 1 2 2 2 2 1 2 2 2
592 594 595 596 597 598 599 600 602 603 605 607 608 609 610 611
2 2 1 2 2 2 2 2 1 2 2 2 2 2 1 1
612 613 614 616 617 618 621 622 623 624 625 628 629 631 632 634
1 2 2 2 2 1 2 2 2 2 2 2 1 1 2 2
635 636 638 639 640 642 643 645 647 649 650 651 652 655 656 659
2 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2
661 662 663 665 666 668 670 671 672 677 678 680 681 682 683 684
2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2
687 690 693 694 695 697 698 699 700 701 706 709 711 713 714 715
2 2 2 1 2 2 2 1 2 2 1 2 1 2 2 2
716 719 723 724 726 727 728 729 730 731 732 733 734 737 738 740
2 2 2 2 2 2 1 2 2 2 2 2 1 2 2 1
741 742 747 748 749 750 752 753 754 759 760 762 763 765 767 768
2 2 1 2 2 2 2 2 1 2 1 1 2 2 2 2
769 772 773 774 775 776 777 778 779 780 782 783 784 785 786 788
2 2 2 2 2 1 2 2 2 2 2 2 2 1 2 2
790 792 794 795 798 799 801 802 803 804 806 807 809 811 812 813
2 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2
814 815 818 819 820 821 822 824 825 827 829 830 832 833 834 836
2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2
838 840 843 844 847 850 852 855 856 857 858 861 863 865 866 868
2 2 2 2 1 2 2 1 2 2 2 2 2 2 1 2
871 872 873 874 876 877 878 880 881 883 884 885 888 889 891 893
2 2 2 1 2 2 2 1 2 1 2 2 2 2 1 2
894 895 896 897 898 900 902 904 905 906 910 911 915 916 919 920
1 2 2 2 2 2 1 2 1 2 2 2 2 1 2 2
922 923 925 926 928 930 931 932 935 937 939 940 942 943 944 946
2 2 2 1 2 2 2 1 1 2 1 2 1 2 1 1
947 948 949 950 951 952 954 956 957 959 961 963 964 965 968 970
1 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1
971 972 973 976 978 979 980 981 982 983 984 985 986 988 990 991
2 2 1 2 2 1 2 2 2 2 1 2 2 1 2 1
994 995 996 997 998 999 1002 1004 1005 1006 1008 1009 1010 1012 1013 1014
2 1 2 1 2 2 2 2 2 2 2 2 2 2 1 2
1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1026 1027 1030 1031 1032 1033
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
1035 1036 1039 1042 1043 1045 1046 1047 1049 1051 1054 1056 1057 1058 1060 1061
2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2
1062 1066 1067 1068 1069 1070 1071 1072 1073 1075 1076 1077 1078 1079 1080 1082
2 2 2 1 2 2 1 1 2 2 1 2 1 2 2 2
1083 1084 1086 1089 1090 1091 1092 1093 1094 1095 1097 1098 1100 1101 1103 1104
2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2
1105 1106 1107 1108 1112 1113 1114 1115 1116 1117 1118 1119 1121 1122 1123 1124
2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2
1127 1128 1130 1131 1132 1133 1134 1135 1136 1139 1140 1143 1144 1146 1147 1148
2 2 1 2 2 2 1 2 2 1 2 2 2 1 2 2
1150 1151 1152 1154 1155 1158 1159 1161 1162 1163 1164 1165 1168 1169 1171 1172
2 2 2 2 2 1 2 2 1 2 1 2 2 2 1 2
1173 1178 1180 1181 1182 1183 1185 1187 1188 1189 1191 1194 1195 1196 1197 1199
1 2 2 2 1 2 2 2 2 2 2 1 2 1 2 2
1202 1203 1204 1207 1210 1211 1217 1219 1220 1221 1222 1223 1224 1225 1226 1227
1 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1
1228 1229 1230 1231 1232 1233 1234 1235 1237 1238 1239 1240 1241 1243 1244 1245
2 2 2 2 2 2 2 1 1 2 2 2 2 1 2 2
1247 1248 1253 1254 1257 1258 1261 1262 1263 1264 1265 1267 1268 1269 1270 1271
2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2
1272 1273 1274 1275 1277 1278 1279 1280 1281 1283 1284 1286 1287 1288 1289 1290
2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1
1292 1293 1294 1295 1296 1297 1298 1300 1302 1304 1305 1306 1310 1311 1312 1313
1 2 2 2 2 2 2 2 2 2 2 2 1 2 2 1
1314 1315 1317 1319 1321 1322 1324 1325 1326 1327 1328 1329 1331 1333 1335 1336
2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2
1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1350 1351 1353 1354 1355 1356
2 2 2 2 1 2 1 2 2 2 2 2 2 2 2 2
1357 1358 1360 1361 1363 1364 1365 1366 1367 1368 1369 1370 1372 1373 1376 1377
2 2 2 1 1 2 2 2 2 1 2 2 2 2 2 2
1378 1379 1380 1381 1383 1385 1387 1388 1389 1393 1394 1395 1396 1397 1398 1399
2 2 1 2 1 2 2 2 2 2 2 2 2 2 2 2
1400 1401 1402 1403 1405 1408 1409 1410 1412 1413 1418 1419 1420 1421 1423 1427
2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2
1428 1429 1430 1431 1432 1435 1436 1437 1438 1440 1441 1442 1443 1444 1445 1446
2 2 2 2 2 2 2 1 2 2 2 2 1 2 2 2
1448 1449 1450 1453 1454 1455 1459 1460 1461 1463 1464 1465 1467 1468 1470 1475
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
1476 1477 1478 1479 1483 1484 1485 1486 1487 1489 1490 1491 1492 1494 1495 1496
1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2
1497 1499 1500 1503 1504 1505 1506 1507 1509 1510 1511 1512 1513 1514 1515 1516
2 2 2 2 2 2 2 2 2 1 2 2 2 1 2 2
1518 1519 1520 1521 1522 1523 1525 1526 1527 1528 1530 1531 1532 1533 1534 1535
2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2
1543 1545 1546 1547 1548 1550 1552 1554 1555 1559 1560 1561 1562 1563 1564 1566
2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 2
1567 1570 1571 1572 1573 1574 1577 1578 1579 1581 1583 1584 1586 1590 1591 1592
2 1 2 2 2 2 2 1 2 1 2 1 2 2 2 2
1593 1594 1595 1596 1597 1598 1599 1601 1602 1603 1605 1606 1607 1608 1609 1610
1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2
1611 1612 1614 1615 1616 1620 1623 1626 1628 1629 1630 1631 1633 1635 1636 1637
2 1 2 2 2 1 2 2 2 2 2 1 2 2 2 1
1638 1640 1642 1643 1644 1646 1647 1648 1650 1651 1652 1653 1654 1656 1657 1658
2 1 1 1 2 2 2 2 2 1 2 2 2 1 2 2
1663 1664 1667 1669 1670 1671 1673 1674 1675 1676 1677 1678 1680 1681 1682 1683
2 1 2 2 2 1 2 2 2 2 2 2 2 2 2 2
1684 1687 1688 1689 1690 1692 1693 1695 1697 1698 1700 1701 1702 1705 1706 1707
2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 1
1708 1709 1711 1713 1718 1719 1721 1722 1723 1724 1725 1728 1729 1730 1733 1734
2 2 1 2 2 2 2 2 2 2 2 2 2 1 1 2
1735 1737 1738 1739 1740 1741 1742 1744 1745 1746 1747 1748 1749 1751 1753 1755
2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2
1756 1757 1758 1759 1760 1761 1762 1763 1768 1769 1770 1771 1772 1773 1774 1775
2 1 2 2 2 2 2 2 2 1 2 2 1 2 2 2
1776 1777 1778 1780 1781 1782 1783 1784 1785 1786 1787 1788 1791 1792 1793 1796
1 2 2 1 2 2 2 2 2 2 2 2 2 2 1 2
1797 1801 1803 1804 1807 1809 1810 1813 1814 1816 1818 1819 1821 1822 1826 1827
2 2 2 1 2 2 1 1 2 2 2 2 2 2 2 2
1828 1829 1830 1832 1833 1836 1837 1839 1844 1847 1850 1851 1855 1856 1857 1858
2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 1
1860 1861 1862 1863 1864 1867 1868 1870 1873 1874 1875 1876 1877 1878 1879 1882
2 1 2 1 2 2 1 2 2 2 2 2 2 2 2 2
1883 1885 1887 1888 1889 1890 1891 1892 1893 1894 1895 1897 1898 1900 1903 1904
2 1 1 1 2 2 2 1 2 2 2 1 2 2 2 2
1905 1906 1908 1910 1911 1912 1913 1914 1917 1918 1920 1921 1922 1923 1924 1925
2 2 1 2 1 2 2 2 2 2 2 2 1 2 2 2
1926 1929 1930 1931 1932 1935 1936 1937 1938 1939 1942 1943 1944 1945 1946 1947
2 2 2 2 1 1 1 2 2 2 1 2 2 2 1 2
1949 1950 1951 1952 1953 1954 1955 1956 1957 1959 1960 1962 1963 1964 1966 1969
2 2 2 2 2 1 2 1 1 2 2 2 2 2 2 2
1970 1972 1973 1975 1976 1977 1978 1980 1981 1982 1987 1990 1991 1992 1993 1994
2 2 2 2 1 2 2 2 1 2 1 1 1 2 2 2
1995 1996 1997 1998 1999 2000 2002 2003 2004 2005 2006 2007 2009 2010 2011 2012
1 1 2 2 2 2 1 2 2 2 2 2 1 2 2 2
2013 2014 2015 2016 2018 2019 2020 2021 2022 2023 2026 2027 2028 2029 2030 2031
2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2
2032 2034 2035 2036 2037 2038 2039 2041 2042 2043 2044 2045 2046 2047 2048 2049
2 2 1 2 2 2 2 2 2 2 2 2 2 2 1 2
2050 2051 2052 2054 2056 2057 2059 2060 2063 2064 2065 2067 2068 2071 2074 2075
1 2 1 2 2 2 2 2 2 2 2 2 1 2 2 2
2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2087 2089 2091 2094 2095 2096
2 1 2 2 2 2 1 2 2 1 2 2 2 2 2 1
2097 2099 2100 2102 2103 2105 2106 2108 2109 2110 2112 2113 2115 2116 2117 2118
2 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2
2119 2120 2121 2122 2123 2124 2125 2126 2127 2129 2130 2132 2133 2134 2135 2137
2 2 1 2 1 2 2 1 2 2 2 1 2 2 2 2
2139 2142 2144 2148 2152 2154 2156 2157 2158 2161 2163 2165 2166 2169 2170 2171
2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2
2172 2174 2175 2176 2177 2178 2181 2182 2183 2184 2185 2186 2187 2188 2190 2191
1 2 2 2 1 2 1 1 2 1 2 2 2 1 2 2
2193 2194 2195 2196 2197 2198 2199 2200 2201 2203 2207 2209 2211 2212 2213 2214
2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2
2215 2216 2217 2218 2221 2222 2223 2224 2225 2226 2228 2229 2230 2231 2232 2233
2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2
2235 2236 2237 2239 2240 2242 2243 2244 2247 2248 2249 2250 2251 2252 2254 2255
2 2 2 2 1 2 2 2 2 2 2 1 2 1 1 1
2256 2257 2258 2259 2260 2261 2262 2263 2264 2265 2266 2267 2270 2271 2272 2273
2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2
2274 2276 2278 2279 2280 2283 2284 2285 2286 2287 2288 2291 2294 2297 2298 2299
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1
2300 2302 2303 2304 2305 2309 2310 2311 2314 2316 2319 2320 2321 2323 2324 2325
1 2 1 2 2 2 2 2 2 2 2 2 2 1 2 2
2327 2328 2329 2330 2331 2332 2333 2334 2335 2336 2338 2339 2340 2342 2344 2345
2 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2
2346 2348 2351 2353 2354 2355 2356 2357 2359 2360 2361 2363 2364 2365 2366 2369
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
2370 2372 2373 2374 2375 2376 2377 2378 2379 2380 2382 2383 2384 2385 2386 2387
2 2 2 1 2 2 2 1 1 2 2 2 2 2 2 2
2388 2391 2392 2393 2394 2395 2398 2400 2402 2403 2405 2406 2407 2410 2411 2412
2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 1
2413 2414 2415 2418 2421 2424 2425 2426 2427 2428 2429 2433 2434 2435 2438 2439
2 2 2 2 2 1 2 2 1 2 1 1 2 1 2 2
2440 2441 2442 2443 2445 2447 2448 2449 2450 2452 2453 2454 2455 2456 2457 2458
1 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2
2460 2461 2462 2463 2464 2465 2466 2467 2471 2472 2474 2476 2477 2478 2479 2480
2 2 2 2 2 2 2 2 2 1 2 1 2 2 2 2
2481 2482 2483 2484 2485 2486 2487 2488 2491 2493 2494 2497 2498 2499 2500 2501
2 1 2 1 2 1 1 2 2 2 2 2 2 2 1 2
2502 2506 2508 2509 2510 2511 2513 2514 2515 2517 2518 2520 2521 2522 2524 2525
1 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2
2526 2527 2529 2530 2531 2533 2536 2538 2539 2540 2542 2543 2547 2548 2549 2551
2 2 2 1 2 2 1 2 2 2 2 2 2 2 2 2
2552 2553 2554 2559 2561 2563 2564 2567 2568 2570 2572 2573 2574 2575 2576 2577
2 2 2 2 2 2 2 2 1 2 2 2 1 2 2 2
2578 2579 2580 2581 2584 2586 2587 2588 2590 2591 2593 2596 2597 2598 2599 2602
2 2 1 2 2 2 2 2 2 2 2 1 2 2 2 2
2603 2605 2606 2608 2609 2611 2612 2614 2615 2616 2617 2619 2620 2622 2623 2624
2 2 2 2 2 2 1 2 2 2 2 2 1 1 2 1
2625 2626 2628 2629 2630 2631 2633 2634 2635 2636 2637 2638 2639 2642 2643 2644
1 1 2 2 2 2 1 2 1 2 2 2 1 2 2 2
2645 2648 2649 2652 2653 2655 2657 2662 2663 2664 2665 2669 2671 2672 2674 2675
2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 1
2676 2677 2678 2679 2681 2682 2684 2685 2688 2689 2690 2691 2692 2693 2697 2699
1 1 1 2 2 2 2 2 2 2 2 2 2 1 2 1
2701 2703 2705 2707 2708 2710 2711 2712 2714 2715 2716 2717 2718 2719 2721 2722
2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2
2724 2725 2726 2727 2728 2731 2732 2733 2734 2735 2736 2738 2739 2741 2742 2745
1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
2746 2748 2750 2752 2755 2756 2757 2758 2760 2761 2762 2763 2764 2765 2767 2768
2 2 2 1 2 2 2 1 1 2 2 2 2 2 1 1
2770 2774 2776 2777 2778 2779 2780 2781 2782 2783 2785 2786 2787 2788 2789 2790
2 2 2 2 2 2 2 2 1 2 1 2 1 2 2 2
2791 2792 2797 2798 2799 2800 2801 2802 2804 2806 2807 2808 2809 2810 2811 2812
2 2 1 2 2 2 1 2 2 2 2 2 2 1 2 2
2813 2814 2815 2816 2817 2818 2819 2820 2823 2824 2825 2826 2827 2828 2829 2830
1 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2
2832 2833 2835 2837 2840 2841 2842 2844 2845 2846 2847 2849 2851 2852 2853 2854
2 2 2 1 2 2 2 2 2 1 2 2 2 1 2 1
2855 2856 2857 2858 2859 2861 2862 2864 2865 2866 2867 2871 2872 2875 2876 2877
2 1 2 1 2 1 2 2 2 2 2 2 1 1 2 2
2879 2880 2881 2882 2884 2885 2886 2887 2890 2891 2892 2893 2896 2897 2898 2899
1 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2
2901 2902 2905 2906 2907 2908 2909 2911 2912 2914 2916 2917 2918 2919 2920 2924
1 1 2 1 2 2 2 2 2 2 2 2 2 2 1 2
2926 2928 2930 2931 2932 2933 2934 2935 2936 2938 2940 2942 2944 2945 2947 2949
2 2 2 2 2 2 2 1 2 2 1 1 2 2 2 2
2950 2953 2955 2956 2957 2959 2960 2962 2965 2966 2968 2969 2971 2972 2973 2975
2 1 2 2 1 2 1 2 2 2 2 2 2 2 2 2
2976 2977 2979 2980 2981 2983 2984 2985 2986 2988 2990 2991 2992 2993 2998 3002
2 2 2 1 1 2 2 2 1 2 2 2 2 2 2 2
3004 3007 3008 3009 3011 3012 3013 3014 3015 3016 3018 3020 3021 3022 3023 3024
2 2 1 2 2 2 2 2 2 2 1 2 2 2 2 2
3025 3027 3029 3030 3032 3034 3037 3038 3044 3045 3047 3048 3053 3055 3056 3057
1 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2
3058 3059 3060 3061 3062 3066 3067 3068 3070 3071 3072 3073 3077 3078 3080 3081
2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2
3082 3084 3087 3088 3092 3094 3095 3096 3097 3099 3100 3102 3104 3105 3106 3107
1 1 1 1 2 2 2 2 2 1 2 2 2 2 2 2
3108 3110 3112 3114 3115 3117 3119 3122 3124 3126 3127 3128 3129 3130 3131 3132
1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 1
3134 3135 3137 3138 3139 3140 3143 3146 3147 3148 3149 3152 3153 3154 3155 3156
2 2 2 1 2 2 2 2 2 2 1 2 1 2 1 2
3157 3158 3161 3163 3166 3168 3170 3171 3172 3173 3174 3176 3177 3178 3182 3184
1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2
3185 3186 3187 3188 3190 3191 3192 3194 3195 3196 3197 3198 3199 3200 3202 3204
1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2
3205 3207 3208 3209 3210 3212 3216 3217 3218 3219 3220 3221 3222 3223 3224 3225
2 2 2 2 2 1 2 1 1 2 2 2 2 2 2 2
3226 3227 3228 3230 3233 3234 3236 3237 3238 3239 3240 3241 3242 3244 3245 3246
2 2 2 2 2 1 2 2 2 2 1 2 2 2 2 2
3247 3249 3251 3252 3254 3257 3259 3261 3262 3264 3265 3266 3267 3268 3269 3272
2 1 2 2 2 2 2 2 2 2 2 2 1 2 2 2
3273 3274 3276 3277 3279 3280 3283 3285 3286 3287 3288 3289 3290 3291 3292 3293
2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1
3294 3295 3297 3299 3300 3301 3302 3304 3305 3307 3308 3310 3311 3314 3315 3318
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
3320 3321 3322 3325 3327 3328 3330 3331 3332 3334 3335 3336 3337 3339 3341 3342
2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 1
3343 3345 3346 3348 3349 3350 3351 3353 3355 3356 3357 3358 3359 3360 3361 3362
2 2 2 2 2 2 2 1 1 2 2 2 2 1 2 2
3363 3366 3367 3368 3369 3371 3372 3373 3374 3375 3377 3378 3380 3381 3384 3386
2 2 2 2 2 2 1 2 2 2 1 2 2 2 2 2
3387 3388 3389 3390 3391 3392 3393 3394 3396 3397 3398 3399 3400 3402 3403 3405
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
3407 3408 3409 3410 3411 3413 3415 3416 3417 3418 3419 3420 3421 3423 3424 3427
1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 1
3431 3432 3433 3434 3435 3436 3437 3438 3439 3440 3441 3442 3445 3446 3448 3449
2 2 2 1 2 1 2 2 2 2 2 2 2 2 2 1
3450 3451 3453 3454 3456 3457 3459 3460 3461 3462 3464 3465 3466 3467 3469 3470
2 2 2 1 2 2 2 1 2 2 2 2 2 2 2 2
3472 3474 3475 3476 3477 3478 3480 3481 3482 3485 3486 3489 3490 3491 3493 3494
2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
3496 3497 3498 3499 3500 3501 3502 3503 3504 3507 3508 3511 3514 3517 3522 3523
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
3529 3532 3534 3535 3536 3537 3541 3542 3543 3545 3546 3547 3548 3550 3551 3552
2 2 2 1 2 2 2 1 2 2 1 2 1 2 2 2
3554 3556 3557 3559 3562 3563 3564 3568 3569 3570 3571 3572 3575 3577 3579 3580
2 2 2 2 1 2 1 2 2 2 1 1 1 2 2 2
3582 3585 3586 3587 3588 3589 3591 3592 3594 3595 3597 3598 3600 3601 3602 3603
1 2 2 2 2 2 1 2 1 2 2 2 2 2 2 1
3605 3606 3607 3609 3610 3612 3613 3614 3615 3616 3617 3620 3621 3622 3623 3624
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
3625 3627 3628 3630 3631 3632 3634 3635 3636 3637 3640 3644 3645 3646 3647 3648
2 2 2 2 2 2 1 2 2 1 2 2 2 2 2 2
3649 3650 3651 3652 3653 3654 3658 3659 3660 3662 3663 3665 3668 3670 3671 3672
2 1 2 2 1 2 2 2 2 2 2 2 2 2 2 1
3674 3675 3678 3679 3681 3684 3685 3687 3688 3689 3691 3692 3693 3694 3695 3696
2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 2
3697 3699 3700 3702 3704 3705 3706 3707 3709 3710 3711 3713 3714 3715 3716 3718
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
3719 3720 3723 3724 3725 3727 3728 3729 3733 3736 3737 3739 3740 3741 3742 3743
1 2 1 2 2 2 1 2 2 2 2 2 2 2 2 2
3746 3748 3750 3751 3752 3753 3754 3756 3757 3758 3759 3760 3762 3765 3767 3768
1 1 2 1 1 2 2 2 2 2 2 1 2 1 2 2
3770 3771 3772 3773 3777 3778 3779 3780 3781 3782 3784 3785 3786 3787 3789 3790
2 2 2 2 2 2 2 1 2 2 2 2 2 1 2 2
3793 3796 3797 3798 3799 3800 3801 3803 3806 3807 3809 3810 3812 3814 3815 3818
2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2
3819 3820 3821 3825 3827 3828 3829 3830 3831 3832 3834 3835 3836 3837 3838 3843
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
3844 3845 3846 3847 3849 3850 3851 3852 3854 3855 3856 3857 3859 3860 3861 3862
2 2 2 2 2 1 2 2 2 2 2 1 2 1 2 2
3863 3865 3867 3869 3870 3871 3873 3875 3877 3878 3879 3880 3881 3883 3884 3885
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
3886 3887 3888 3889 3890 3891 3892 3893 3897 3899 3900 3902 3903 3904 3905 3907
2 1 2 2 1 1 2 2 2 1 2 1 2 1 2 2
3908 3910 3911 3912 3913 3914 3916 3917 3919 3920 3921 3922 3923 3924 3925 3926
2 1 2 2 1 2 1 2 1 2 2 2 2 2 1 2
3927 3928 3929 3931 3933 3934 3935 3936 3938 3939 3940 3941 3944 3945 3946 3948
2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2
3949 3950 3951 3952 3954 3955 3956 3958 3961 3962 3963 3964 3967 3968 3969 3970
2 1 2 2 2 2 2 2 2 2 1 2 2 2 2 2
3971 3973 3974 3975 3976 3977 3978 3979 3981 3986 3987 3988 3989 3990 3991 3992
2 2 1 2 2 2 2 2 2 2 1 2 1 1 2 2
3996 3997 3998 3999 4000 4001 4002 4003 4004 4007 4008 4009 4010 4011 4012 4013
2 1 2 2 2 2 1 1 2 2 1 2 1 2 2 2
4015 4016 4018 4021 4022 4023 4025 4026 4027 4028 4030 4032 4033 4036 4037 4038
2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2
4040 4042 4043 4045 4048 4049 4051 4052 4054 4055 4056 4057 4059 4060 4061 4065
2 1 1 2 2 2 1 2 2 2 2 2 2 2 2 2
4067 4068 4069 4071 4074 4075 4076 4078 4079 4080 4081 4083 4085 4093 4094 4095
1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
4096 4097 4098 4099 4101 4102 4103 4105 4106 4107 4108 4109 4111 4112 4113 4115
1 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2
4116 4118 4119 4120 4121 4123 4125 4126 4127 4128 4130 4134 4136 4137 4138 4139
1 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2
4140 4141 4142 4143 4144 4145 4146 4147 4148 4149 4150 4151 4152 4153 4154 4158
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1
4159 4160 4163 4164 4166 4167 4168 4169 4171 4174 4175 4176 4177 4178 4179 4180
2 2 2 2 2 2 1 2 2 2 2 1 2 2 2 2
4181 4182 4184 4187 4188 4189 4191 4192 4193 4194 4196 4197 4198 4200 4201 4203
2 2 2 2 2 2 1 2 1 2 2 2 1 2 2 1
4206 4208 4209 4210 4212 4214 4215 4216 4217 4218 4220 4221 4225 4226 4228 4231
2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 1
4232 4233 4234 4235 4236 4238 4239 4240 4242 4243 4245 4246 4247 4252 4253 4255
1 2 2 2 2 2 1 1 1 2 2 2 1 2 2 2
4257 4258 4259 4260 4261 4263 4264 4265 4266 4267 4268 4269 4270 4272 4274 4275
2 2 2 2 2 1 2 1 2 2 2 2 1 1 2 2
4276 4278 4279 4281 4285 4286 4287 4288 4289 4290 4292 4293 4295 4296 4298 4299
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1
4300 4301 4302 4303 4305 4307 4309 4310 4311 4313 4314 4315 4316 4317 4318 4319
2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2
4320 4321 4322 4326 4328 4330 4331 4332 4334 4336 4337 4340 4341 4345 4346 4348
2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2
4349 4350 4351 4352 4354 4355 4357 4358 4359 4360 4361 4362 4363 4364 4365 4366
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
4367 4368 4369 4370 4372 4373 4375 4377 4379 4380 4381 4382 4383 4384 4385 4386
2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 2
4389 4390 4392 4393 4395 4396 4398 4399 4400 4402 4403 4404 4406 4408 4409 4411
2 2 2 2 2 2 1 2 2 2 1 2 2 2 2 2
4412 4414 4415 4417 4418 4419 4420 4421 4425 4426 4427 4428 4429 4432 4433 4434
2 2 2 2 2 2 2 2 1 2 1 1 2 2 2 2
4436 4437 4438 4440 4441 4443 4444 4445 4446 4447 4449 4450 4451 4452 4454 4458
2 1 2 2 2 1 2 1 2 2 2 2 2 2 2 2
4459 4460 4462 4464 4465 4466 4467 4468 4469 4471 4472 4474 4475 4476 4477 4480
2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2
4482 4483 4484 4485 4486 4487 4489 4491 4492 4493 4494 4496 4500 4501 4502 4503
2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
4504 4506 4507 4509 4510 4511 4513 4515 4516 4517 4518 4519 4520 4524 4525 4526
2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2
4528 4530 4531 4533 4534 4535 4536 4537 4541 4543 4545 4546 4547 4550 4551 4553
2 2 2 2 1 1 2 2 2 2 2 2 1 1 1 2
4557 4558 4559 4561 4562 4565 4566 4567 4568 4569 4570 4571 4572 4574 4575 4576
2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2
4577 4578 4579 4582 4583 4585 4587 4588 4589 4590 4591 4593 4594 4595 4596 4597
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
4598 4599 4601 4602 4604 4605 4606 4607 4608 4610 4611 4612 4613 4615 4616 4617
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
4619 4620 4622 4623 4628 4629 4630 4631 4632 4633 4634 4635 4636 4637 4638 4640
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
4642 4643 4645 4646 4647 4651 4652 4653 4654 4656 4657 4658 4659 4661 4663 4664
1 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2
4666 4668 4669 4671 4672 4673 4675 4676 4677 4679 4680 4681 4682 4683 4684 4685
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
4686 4687 4688 4689 4690 4691 4692 4696 4698 4702 4703 4705 4706 4707 4708 4709
1 1 2 2 2 2 2 2 2 1 1 2 2 1 1 2
4711 4712 4713 4714 4717 4718 4719 4720 4721 4723 4724 4726 4728 4729 4730 4731
2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
4732 4733 4734 4735 4736 4737 4738 4739 4740 4742 4745 4746 4749 4750 4751 4752
2 2 2 2 2 1 2 2 2 2 2 1 2 2 2 2
4754 4755 4756 4757 4758 4761 4762 4763 4764 4765 4766 4770 4771 4772 4773 4775
2 2 2 2 1 1 2 2 2 2 1 2 2 2 1 2
4777 4779 4780 4781 4782 4783 4784 4785 4786 4787 4788 4791 4792 4793 4795 4797
2 2 2 2 1 2 2 2 2 2 2 2 2 1 2 1
4798 4799 4800 4801 4802 4803 4804 4805 4806 4809 4811 4812 4813 4814 4816 4817
2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2
4818 4819 4821 4823 4824 4825 4826 4827 4828 4829 4830 4831 4832 4834 4835 4838
2 2 2 2 1 2 2 2 2 2 2 1 2 1 2 2
4839 4840 4844 4845 4847 4849 4850 4851 4853 4854 4855 4857 4858 4859 4860 4862
2 2 1 2 2 2 2 2 1 2 2 2 2 2 2 2
4863 4864 4865 4868 4869 4870 4872 4873 4874 4876 4878 4881 4882 4883 4884 4885
1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2
4886 4889 4890 4892 4894 4895 4901 4902 4904 4906 4907 4908 4909 4910 4912 4913
2 1 2 2 2 2 2 1 2 2 2 1 2 2 2 2
4914 4917 4918 4920 4921 4923 4924 4925 4927 4928 4929 4930 4931 4932 4934 4935
2 2 1 1 2 2 2 2 2 1 2 2 2 2 2 2
4936 4938 4940 4941 4945 4947 4948 4949 4951 4952 4954 4955 4956 4957 4959 4960
2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2
4961 4964 4966 4967 4969 4971 4972 4973 4975 4980 4981 4982 4983 4984 4986 4987
2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
4989 4990 4991 4993 4995 4998 4999 5000 5001 5002 5003 5005 5007 5008 5009 5011
2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2
5012 5013 5014 5017 5018 5019 5020 5021 5023 5024 5027 5028 5029 5030 5033 5034
2 2 2 2 2 2 2 2 1 1 1 2 2 1 1 2
5035 5036 5037 5038 5041 5043 5045 5047 5048 5049 5050 5051 5053 5054 5055 5057
1 1 2 1 1 2 1 2 1 2 2 1 2 2 2 2
5058 5061 5062 5063 5064 5065 5067 5068 5069 5070 5073 5074 5076 5077 5079 5080
1 2 2 1 1 2 2 2 2 1 2 2 2 2 2 2
5081 5084 5085 5089 5090 5095 5097 5098 5101 5102 5103 5105 5106 5108 5109 5110
2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2
5111 5112 5113 5114 5115 5116 5118 5120 5122 5123 5124 5125 5127 5128 5129 5130
2 1 2 2 2 1 1 1 2 2 2 2 2 2 2 2
5131 5132 5133 5135 5138 5140 5142 5143 5144 5147 5149 5151 5152 5153 5154 5156
2 1 2 2 2 2 1 2 2 1 2 2 2 2 2 2
5157 5158 5159 5160 5161 5162 5165 5166 5167 5169 5170 5171 5175 5177 5178 5179
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
5180 5183 5184 5185 5186 5188 5189 5190 5191 5192 5193 5194 5195 5196 5199 5200
2 2 2 2 2 2 2 2 2 1 2 2 1 2 2 1
5202 5203 5204 5205 5206 5207 5208 5209 5211 5213 5215 5216 5217 5218 5219 5222
2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2
5224 5226 5228 5231 5234 5236 5237 5239 5240 5241 5243 5244 5245 5246 5248 5249
2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2
5251 5253 5255 5256 5257 5258 5259 5262 5265 5266 5269 5270 5272 5273 5274 5275
2 2 2 2 2 2 1 2 2 1 2 2 2 1 2 2
5276 5277 5279 5280 5282 5283 5284 5285 5286 5287 5288 5289 5290 5291 5292 5293
1 2 2 2 1 2 2 1 2 2 1 2 2 2 2 2
5294 5295 5296 5297 5298 5299 5301 5302 5309 5311 5312 5313 5314 5315 5317 5319
2 2 1 2 2 2 1 1 1 2 2 2 2 2 2 2
5321 5323 5326 5327 5328 5329 5330 5334 5335 5336 5337 5339 5341 5342 5343 5344
2 2 1 2 1 2 2 2 2 2 2 2 2 2 2 2
5345 5346 5347 5351 5352 5353 5354 5355 5357 5359 5360 5361 5362 5363 5365 5366
2 1 2 2 2 2 2 1 2 1 1 1 1 2 2 2
5367 5370 5371 5374 5375 5376 5377 5379 5382 5385 5386 5387 5388 5390 5391 5393
1 2 2 2 2 1 2 2 2 1 2 2 2 2 2 2
5395 5396 5397 5398 5399 5400 5401 5402 5403 5404 5405 5406 5407 5408 5409 5410
2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2
5411 5412 5413 5414 5416 5418 5419 5420 5421 5422 5424 5425 5426 5427 5428 5429
2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2
5431 5432 5434 5437 5438 5439 5440 5441 5442 5443 5444 5445 5447 5450 5452 5454
2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2
5455 5457 5459 5460 5461 5466 5468 5469 5470 5471 5472 5474 5475 5476 5477 5478
1 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2
5480 5481 5485 5486 5489 5490 5491 5494 5495 5496 5498 5499 5500 5502 5506 5507
2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2
5508 5509 5510 5511 5512 5513 5514 5515 5516 5517 5518 5521 5522 5523 5525 5526
2 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2
5528 5529 5530 5531 5533 5534 5536 5537 5539 5540 5541 5543 5544 5545 5547 5550
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
5551 5552 5554 5555 5556 5558 5559 5561 5562 5563 5564 5565 5566 5567 5569 5571
2 2 2 2 1 2 2 2 2 1 2 2 1 1 2 2
5572 5573 5574 5575 5576 5577 5578 5580 5582 5583 5584 5585 5587 5588 5590 5591
1 2 2 1 2 2 2 1 2 2 1 1 1 2 2 2
5592 5593 5594 5596 5597 5598 5599 5601 5602 5603 5604 5606 5607 5609 5610 5612
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
5614 5616 5617 5618 5620 5621 5622 5625 5627 5628 5629 5631 5633 5634 5637 5638
2 1 2 2 1 2 2 2 2 2 2 2 2 1 1 2
5640 5642 5644 5645 5647 5649 5651 5652 5655 5656 5658 5659 5660 5661 5662 5663
2 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2
5664 5665 5666 5668 5669 5670 5671 5672 5673 5674 5675 5677 5678 5679 5681 5682
2 2 2 2 2 2 2 1 2 1 2 2 2 2 1 2
5683 5684 5686 5687 5688 5689 5690 5695 5696 5697 5698 5699 5701 5702 5706 5707
2 2 2 2 2 1 2 2 2 1 2 2 2 1 2 2
5708 5709 5710 5711 5712 5714 5718 5721 5722 5723 5724 5726 5727 5728 5733 5734
2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2
5735 5736 5738 5741 5742 5743 5745 5748 5749 5750 5753 5755 5756 5758 5759 5760
2 2 2 2 2 2 2 2 1 2 2 2 2 2 1 2
5763 5764 5766 5767 5768 5769 5770 5771 5774 5775 5776 5777 5778 5779 5781 5782
2 1 1 2 2 2 2 2 2 1 2 2 2 2 2 2
5784 5785 5788 5789 5790 5792 5793 5794 5796 5797 5798 5799 5800 5802 5803 5805
2 1 1 2 1 1 2 2 2 2 2 2 2 2 1 1
5806 5807 5810 5813 5821 5822 5823 5824 5825 5827 5830 5831 5834 5835 5837 5838
1 1 1 2 2 2 2 2 2 2 2 1 2 1 2 2
5842 5844 5845 5846 5847 5848 5849 5850 5851 5853 5855 5861 5862 5863 5864 5865
2 2 2 2 2 1 2 2 2 2 2 2 2 1 2 2
5866 5867 5870 5871 5873 5874 5875 5876 5878 5879 5880 5882 5883 5884 5885 5886
2 2 2 2 2 2 2 1 1 1 2 1 2 1 2 2
5889 5891 5892 5893 5894 5895 5896 5897 5898 5899 5900 5901 5903 5904 5905 5907
1 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2
5908 5909 5911 5912 5914 5915 5916 5917 5918 5920 5921 5923 5924 5926 5927 5929
2 2 2 1 1 2 2 2 2 2 2 2 1 2 2 2
5930 5931 5932 5933 5934 5935 5937 5938 5940 5942 5945 5946 5947 5949 5950 5951
2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2
5953 5954 5955 5956 5957 5958 5959 5960 5961 5962 5963 5968 5971 5972 5973 5974
2 2 2 2 1 2 2 2 2 2 2 2 1 2 2 1
5976 5978 5979 5980 5981 5982 5983 5984 5985 5986 5989 5990 5991 5992 5995 5997
2 2 2 2 1 2 1 2 2 2 2 2 2 1 2 2
5998 5999 6000 6001 6002 6003 6005 6008 6009 6010 6012 6014 6015 6017 6019 6021
2 2 2 2 2 1 2 2 1 2 2 2 1 2 1 2
6023 6024 6025 6027 6028 6029 6030 6033 6034 6035 6036 6037 6041 6043 6044 6045
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6049 6050 6051 6052 6054 6060 6061 6062 6063 6064 6065 6066 6067 6068 6069 6072
2 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2
6073 6074 6075 6076 6077 6078 6081 6082 6083 6085 6086 6092 6093 6094 6095 6096
2 1 2 1 2 2 2 2 2 2 2 1 2 2 2 2
6098 6101 6102 6104 6105 6106 6107 6108 6109 6111 6112 6114 6116 6118 6120 6122
2 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2
6123 6124 6127 6129 6130 6134 6135 6136 6138 6139 6140 6141 6142 6144 6147 6148
2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2
6150 6152 6153 6154 6156 6157 6158 6159 6162 6163 6165 6167 6168 6170 6171 6172
2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2
6175 6177 6179 6180 6182 6184 6185 6186 6187 6188 6189 6191 6193 6196 6200 6202
1 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2
6203 6204 6206 6208 6211 6212 6213 6214 6216 6217 6218 6219 6220 6221 6222 6224
2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2
6225 6228 6229 6230 6231 6232 6234 6237 6239 6240 6242 6243 6246 6247 6250 6251
2 2 2 1 1 2 2 2 2 2 2 2 1 2 2 2
6252 6253 6254 6255 6260 6261 6262 6263 6264 6268 6270 6271 6272 6274 6276 6277
2 2 2 2 2 2 2 2 2 2 1 2 1 2 2 1
6278 6279 6280 6282 6283 6284 6285 6286 6287 6289 6290 6292 6294 6296 6297 6298
2 1 2 1 2 1 2 2 2 2 1 1 2 2 2 2
6299 6300 6302 6303 6304 6305 6306 6307 6309 6311 6312 6313 6315 6317 6319 6321
2 2 2 2 1 2 2 1 2 2 2 1 2 2 1 2
6322 6323 6324 6325 6327 6328 6329 6330 6333 6334 6335 6338 6341 6343 6345 6346
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6347 6349 6350 6351 6352 6354 6358 6359 6360 6361 6362 6363 6364 6365 6367 6369
2 2 2 2 2 1 2 1 2 2 1 2 2 2 1 2
6370 6371 6372 6374 6376 6377 6378 6379 6380 6382 6383 6384 6385 6386 6387 6388
1 2 1 2 2 2 2 2 2 2 2 2 2 1 2 2
6389 6392 6394 6395 6396 6397 6399 6402 6403 6404 6405 6406 6407 6408 6411 6413
1 1 1 2 2 1 1 2 2 2 2 2 2 2 2 2
6414 6417 6418 6419 6420 6422 6423 6424 6425 6426 6428 6429 6430 6431 6432 6433
2 1 1 2 2 2 1 2 2 1 2 2 2 2 2 2
6434 6436 6438 6439 6440 6441 6444 6445 6446 6448 6451 6452 6453 6456 6457 6458
1 2 2 2 2 2 2 1 2 2 2 1 2 2 2 1
6461 6462 6463 6466 6467 6469 6470 6471 6472 6473 6474 6475 6476 6477 6479 6484
2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
6485 6486 6488 6489 6490 6491 6492 6493 6494 6495 6496 6497 6498 6499 6500 6502
1 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
6504 6506 6507 6510 6511 6513 6514 6516 6519 6520 6526 6527 6530 6531 6533 6534
1 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2
6535 6536 6537 6538 6539 6540 6541 6543 6544 6545 6546 6548 6550 6551 6554 6555
2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2
6556 6557 6558 6560 6562 6564 6565 6566 6567 6568 6570 6571 6572 6575 6578 6579
2 2 2 1 1 1 2 2 2 1 2 2 2 2 2 2
6580 6582 6583 6584 6585 6587 6590 6591 6592 6593 6595 6596 6598 6599 6600 6602
2 2 2 2 2 2 2 2 2 2 1 2 1 2 2 2
6603 6604 6605 6607 6608 6609 6610 6611 6612 6614 6616 6617 6618 6620 6621 6622
2 2 2 2 2 2 2 1 1 2 2 2 2 1 2 2
6624 6625 6626 6627 6629 6630 6631 6632 6635 6636 6637 6639 6643 6644 6647 6648
2 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2
6650 6651 6653 6656 6657 6658 6659 6660 6662 6664 6667 6668 6671 6672 6675 6677
1 2 2 2 2 1 2 1 1 2 2 2 2 2 2 2
6678 6680 6681 6683 6684 6685 6687 6688 6689 6691 6692 6693 6694 6695 6697 6699
2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2
6701 6703 6704 6706 6707 6709 6711 6713 6714 6715 6717 6719 6721 6723 6724 6725
1 2 1 2 2 2 2 2 1 2 2 2 2 2 2 2
6726 6731 6732 6733 6735 6736 6738 6740 6743 6744 6745 6746 6748 6749 6750 6751
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6752 6753 6754 6755 6757 6758 6759 6761 6763 6764 6767 6768 6771 6773 6774 6777
2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 2
6778 6779 6780 6781 6782 6783 6784 6785 6786 6787 6788 6789 6793 6794 6796 6798
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1
6799 6800 6802 6803 6805 6806 6807 6811 6814 6818 6819 6820 6822 6823 6825 6826
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6827 6828 6829 6832 6835 6837 6838 6839 6840 6842 6845 6846 6847 6848 6850 6851
2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 1
6852 6853 6854 6855 6856 6857 6858 6860 6861 6864 6866 6867 6868 6869 6870 6871
1 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2
6872 6873 6874 6875 6876 6877 6878 6879 6880 6881 6882 6883 6884 6885 6887 6888
2 2 2 2 2 1 2 2 2 1 2 2 2 2 2 2
6889 6890 6891 6893 6894 6895 6897 6899 6901 6904 6905 6906 6907 6909 6910 6912
2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6913 6914 6915 6916 6917 6918 6919 6920 6922 6923 6924 6925 6926 6927 6928 6931
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6933 6934 6935 6938 6939 6940 6941 6942 6944 6945 6946 6948 6949 6951 6952 6954
2 2 2 2 2 2 2 2 2 1 2 1 2 2 2 2
6955 6956 6958 6962 6967 6969 6971 6973 6974 6977 6979 6980 6981 6982 6984 6985
2 1 2 1 2 2 2 1 2 2 2 2 2 1 2 2
6986 6990 6991 6993 6994 6997 6998 6999 7000 7001 7002 7004 7005 7007 7008 7012
2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1
7013 7014 7015 7017 7019 7020 7022 7023 7024 7027 7028 7029 7030 7031 7032 7033
2 2 1 2 2 1 2 2 2 2 2 2 1 2 2 2
7034 7036 7037 7040 7041 7042 7043 7045 7046 7047 7048 7049 7050 7051 7052 7053
2 2 2 2 2 2 2 2 2 1 2 2 2 1 2 2
7056 7059 7060 7061 7063 7064 7066 7067 7068 7069 7070 7071 7072 7073 7075 7076
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
7077 7078 7080 7082 7083 7084 7085 7088 7089 7092 7093 7095 7096 7097 7098 7099
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
7101 7102 7103 7104 7105 7106 7107 7108 7111 7114 7115 7116 7117 7118 7119 7120
2 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2
7121 7122 7123 7125 7126 7127 7129 7130 7131 7132 7135 7136 7137 7138 7139 7140
2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 2
7141 7142 7143 7144 7145 7147 7148 7151 7152 7153 7154 7155 7157 7158 7160 7161
2 1 2 1 1 2 2 2 2 2 2 2 2 1 2 2
7162 7163 7166 7168 7169 7172 7173 7174 7176 7177 7179 7181 7182 7183 7184 7185
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
7188 7189 7192 7193 7194 7199 7200 7201 7205 7206 7207 7208 7209 7211 7213 7214
2 2 2 1 1 2 2 2 1 2 2 2 2 2 2 2
7216 7218 7219 7220 7221 7223 7225 7226 7227 7230 7231 7232 7234 7235 7236 7237
1 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2
7240 7241 7242 7243 7244 7245 7246 7248 7250 7251 7252 7254 7256 7257 7258 7259
1 2 1 2 2 2 2 2 2 2 1 2 2 1 2 2
7260 7261 7262 7265 7266 7267 7268 7269 7270 7271 7272 7273 7274 7276 7277 7280
2 2 2 1 2 2 1 1 1 2 2 2 2 2 2 2
7281 7285 7286 7287 7289 7290 7291 7293 7294 7295 7296 7297 7299 7302 7306 7308
2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2
7309 7310 7311 7313 7314 7315 7316 7318 7319 7320 7321 7322 7324 7327 7330 7332
2 2 2 1 2 2 1 2 2 2 2 2 2 1 1 2
7336 7337 7338 7339 7340 7341 7342 7343 7345 7346 7347 7348 7350 7353 7354 7356
2 2 2 2 1 2 2 2 2 2 2 2 1 2 2 2
7360 7361 7363 7365 7367 7368 7369 7370 7371 7372 7373 7374 7376 7377 7379 7384
2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2
7385 7386 7388 7389 7393 7394 7395 7396 7397 7398 7400 7403 7404 7405 7406 7407
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
7410 7415 7416 7417 7421 7422 7423 7424 7428 7429 7430 7432 7434 7435 7436 7437
2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2
7438 7439 7441 7444 7447 7448 7449 7450 7451 7452 7453 7454 7455 7456 7457 7459
2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2
7460 7462 7464 7466 7467 7468 7469 7470 7472 7473 7474 7475 7476 7477 7478 7479
1 2 1 1 2 2 2 1 2 2 2 2 2 2 2 2
7481 7482 7484 7485 7487 7488 7493 7497 7498 7505 7506 7507 7508 7509 7510 7511
2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2
7512 7513 7514 7515 7517 7518 7519 7521 7522 7523 7525 7526 7527 7528 7529 7531
2 2 2 1 2 1 2 2 2 2 2 2 2 2 2 2
7534 7540 7541 7542 7543 7546 7549 7550 7551 7552 7553 7555 7556 7557 7558 7559
1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2
7560 7561 7562 7563 7567 7568 7570 7573 7574 7575 7576 7578 7580 7582 7584 7586
1 1 1 2 2 2 2 2 2 2 2 2 2 1 2 2
7587 7588 7590 7591 7592 7594 7595 7596 7597 7598 7600 7601 7603 7605 7606 7608
2 1 2 1 2 2 2 2 2 2 2 2 1 2 2 2
7609 7611 7612 7613 7614 7615 7616 7617 7619 7620 7623 7625 7627 7628 7629 7630
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
7631 7632 7633 7634 7635 7637 7638 7641 7642 7643 7645 7646 7648 7649 7650 7651
2 2 2 1 2 2 1 2 2 2 1 1 2 2 2 2
7652 7653 7656 7657 7658 7659 7660 7661 7663 7664 7665 7666 7669 7670 7671 7672
2 2 2 2 2 2 2 2 2 2 2 1 2 2 1 2
7673 7674 7675 7677 7678 7679 7680 7681 7684 7685 7686 7687 7689 7690 7692 7693
2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2
7694 7695 7697 7699 7700 7701 7702 7703 7705 7706 7708 7709 7711 7712 7713 7714
2 2 1 2 2 2 2 2 2 1 2 1 2 2 2 1
7718 7719 7720 7721 7722 7724 7726 7728 7729 7732 7733 7734 7737 7738 7739 7741
2 2 2 1 2 1 1 1 1 2 2 2 2 2 2 2
7742 7743 7744 7745 7746 7747 7749 7750 7751 7752 7753 7754 7758 7764 7766 7769
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
7770 7771 7772 7773 7776 7777 7778 7779 7782 7783 7787 7788 7791 7792 7794 7795
2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2
7796 7798 7801 7802 7803 7804 7805 7806 7807 7808 7809 7810 7812 7814 7815 7818
2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2
7819 7820 7821 7823 7824 7825 7826 7827 7828 7829 7830 7832 7833 7834 7836 7837
2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2
7838 7840 7842 7843 7844 7845 7846 7847 7849 7851 7853 7854 7855 7856 7857 7860
2 2 2 2 1 2 2 2 2 2 2 2 1 1 2 2
7861 7863 7864 7866 7867 7869 7871 7872 7874 7876 7877 7878 7879 7880 7881 7882
2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
7883 7884 7885 7886 7887 7888 7889 7890 7891 7892 7894 7895 7896 7898 7899 7900
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
7903 7905 7906 7907 7908 7909 7910 7911 7913 7914 7917 7919 7920 7921 7922 7923
2 1 2 2 2 2 2 2 2 2 2 2 1 2 2 2
7925 7926 7929 7930 7931 7932 7935 7936 7937 7938 7943 7945 7946 7949 7950 7951
1 2 2 2 1 2 2 1 1 1 2 2 2 2 1 1
7953 7954 7956 7957 7958 7959 7962 7963 7964 7965 7966 7968 7969 7971 7972 7973
2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2
7974 7976 7977 7978 7979 7981 7982 7983 7985 7989 7990 7991 7993 7994 7996 7999
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
8000 8001 8002 8004 8005 8006 8008 8009 8010 8011 8013 8014 8015 8016 8017 8018
2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2
8019 8020 8022 8023 8025 8026 8027 8028 8030 8031 8032 8033 8034 8035 8036 8038
2 2 1 2 1 2 2 2 2 1 2 2 1 1 2 2
8039 8040 8042 8043 8044 8046 8048 8049 8050 8051 8053 8055 8056 8057 8058 8059
2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 1
8061 8062 8063 8064 8066 8068 8069 8070 8073 8074 8075 8076 8077 8078 8079 8080
2 2 2 2 2 2 2 2 2 2 2 1 1 1 2 2
8083 8084 8085 8086 8087 8088 8089 8090 8093 8094 8097 8100 8101 8102 8103 8104
2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2
8105 8106 8107 8109 8110 8111 8112 8113 8115 8117 8118 8122 8124 8125 8126 8127
2 2 2 2 2 2 1 2 1 2 2 2 2 2 2 2
8128 8130 8131 8133 8134 8135 8136 8138 8139 8140 8142 8143 8147 8148 8150 8151
2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1
8152 8153 8155 8156 8157 8159 8160 8161 8163 8164 8166 8167 8170 8171 8172 8173
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
8174 8175 8177 8179 8180 8181 8182 8183 8184 8185 8186 8187 8188 8189 8190 8191
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
8194 8195 8196 8197 8199 8200 8202 8203 8204 8206 8207 8208 8210 8211 8212 8213
2 2 2 1 2 2 2 1 2 2 1 2 2 2 2 2
8214 8215 8216 8217 8218 8219 8221 8222 8223 8224 8225 8226 8230 8231 8232 8234
2 2 2 2 2 1 2 2 1 1 2 2 2 1 2 2
8236 8237 8239 8240 8241 8242 8244 8245 8246 8248 8249 8250 8253 8254 8255 8256
2 1 1 1 2 1 2 2 1 2 2 1 2 2 1 2
8257 8259 8260 8262 8263 8267 8268 8269 8270 8271 8273 8274 8275 8277 8278 8279
2 2 2 2 2 2 1 2 2 2 1 2 2 2 2 2
8280 8281 8283 8284 8285 8286 8287 8288 8289 8291 8292 8293 8294 8295 8296 8297
2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 1
8298 8299 8300 8303 8306 8308 8311 8314 8317 8318 8319 8320 8321 8322 8323 8325
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
8326 8327 8329 8330 8331 8333 8334 8336 8337 8338 8339 8341 8342 8347 8349 8350
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
8351 8352 8353 8354 8358 8360 8361 8363 8364 8365 8366 8368 8369 8370 8371 8372
2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
8373 8375 8376 8377 8378 8379 8380 8382 8383 8384 8387 8388 8390 8392 8393 8394
2 2 2 2 1 1 2 2 1 2 2 1 1 2 2 1
8395 8396 8399 8400 8401 8402 8405 8406 8408 8409 8410 8412 8413 8414 8415 8416
2 2 2 2 2 2 2 2 1 1 1 2 2 2 2 2
8418 8419 8421 8422 8423 8424 8425 8426 8428 8429 8430 8431 8434 8435 8436 8437
2 2 2 2 1 2 2 2 1 1 2 2 2 1 2 2
8440 8442 8443 8444 8445 8446 8450 8452 8454 8455 8456 8458 8459 8463 8464 8465
2 1 2 2 2 2 2 2 1 2 2 1 2 2 2 1
8466 8467 8468 8469 8470 8472 8474 8476 8477 8478 8479 8481 8483 8487 8488 8489
1 2 2 2 1 2 2 2 2 2 2 1 2 1 1 1
8490 8491 8492 8493 8495 8496 8497 8500 8501 8503 8504 8506 8507 8508 8511 8514
2 1 2 2 2 2 2 1 2 2 2 2 2 2 2 2
8515 8516 8517 8518 8519 8520 8521 8522 8525 8526 8527 8528 8529 8532 8534 8536
1 1 2 2 2 2 2 2 2 2 2 1 2 2 2 2
8537 8538 8541 8542 8543 8545 8546 8547 8548 8549 8550 8551 8553 8555 8556 8557
2 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2
8560 8561 8562 8563 8564 8565 8569 8570 8571 8572 8573 8574 8575 8577 8578 8579
2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 1
8583 8584 8588 8589 8591 8592 8594 8595 8598 8600 8601 8602 8603 8605 8607 8608
2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2
8609 8610 8611 8612 8614 8615 8617 8620 8621 8622 8623 8625 8626 8627 8629 8631
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
8632 8633 8635 8636 8643 8645 8646 8647 8650 8653 8654 8655 8656 8657 8658 8662
2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
8664 8665 8666 8668 8669 8670 8672 8673 8674 8675 8676 8677 8678 8680 8681 8687
1 2 2 2 2 1 2 2 1 2 2 2 2 2 2 1
8689 8691 8692 8694 8695 8697 8698 8703 8704 8705 8707 8708 8710 8711 8715 8718
1 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2
8719 8722 8723 8725 8726 8728 8729 8731 8732 8733 8734 8735 8737 8738 8740 8743
2 2 2 2 1 2 2 2 1 2 2 2 2 2 2 2
8744 8745 8746 8748 8749 8751 8753 8754 8755 8756 8757 8758 8760 8761 8763 8764
2 2 2 2 2 2 1 1 1 2 2 2 2 2 1 2
8765 8766 8767 8768 8769 8770 8772 8775 8776 8777 8779 8780 8781 8782 8783 8784
1 2 2 1 1 2 2 2 2 2 2 2 1 2 1 2
8786 8787 8788 8789 8790 8791 8793 8795 8796 8799 8800 8801 8802 8803 8804 8807
2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 1
8808 8809 8810 8812 8814 8815 8816 8817 8818 8819 8821 8822 8823 8824 8826 8827
2 2 2 2 2 2 2 1 2 2 2 1 2 2 2 2
8828 8829 8831 8832 8835 8839 8840 8842 8845 8846 8849 8850 8853 8854 8855 8856
2 2 2 2 2 2 1 2 2 2 1 2 2 2 2 2
8857 8858 8861 8862 8863 8868 8869 8871 8872 8873 8874 8875 8876 8878 8879 8880
2 2 2 2 2 2 2 2 1 2 2 2 2 2 1 1
8881 8883 8884 8885 8886 8889 8890 8893 8894 8897 8899 8900 8903 8904 8906 8908
2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2
8909 8912 8913 8914 8916 8918 8919 8920 8922 8923 8924 8925 8926 8927 8928 8929
2 2 2 1 2 1 2 1 2 2 2 2 2 2 1 2
8931 8933 8936 8938 8939 8942 8944 8945 8946 8947 8949 8950 8951 8954 8955 8957
2 2 1 2 1 2 2 2 2 2 2 2 1 2 2 2
8958 8960 8961 8962 8963 8964 8965
2 2 2 2 2 2 2
Within cluster sum of squares by cluster:
[1] 24349805 37653165
(between_SS / total_SS = 31.6 %)
Available components:
[1] "cluster" "centers" "totss" "withinss" "tot.withinss"
[6] "betweenss" "size" "iter" "ifault" table(df$fibroscan_cirrhosis, df.kmeans$cluster)
1 2
Cases 29 80
Controls 966 5044centers <- as.data.frame(df.kmeans$centers)
ggplot(data = df) +
geom_point(aes(body_bmi, ha1c,
color = factor(df.kmeans$cluster))) +
geom_point(data = centers, aes(body_bmi, ha1c),
color = "purple", size = 2)
Unsupervised Machine Learning using hierarchical clustering (removing the last 2 columns #31 and #32 as they are the phenotype columns)
df.hclust <- hclust(dist(df), method = "complete")Warning in dist(df): NAs introduced by coerciondf.dend <- dendro_data(as.dendrogram(df.hclust))
labels <- label(df.dend)
labels$fibroscan_steatosis <- df$fibroscan_steatosis[as.numeric(labels$label)]
plot15 <- ggplot(segment(df.dend)) +
geom_segment(aes(x = x, y = y, xend = xend, yend = yend)) +
geom_text(data = labels, aes(label = label, x = x, y = 0,
color = fibroscan_steatosis), size = 4)
plot15
df.cut <- cutree(df.hclust, 11) #Cut where there are 11 clusters
df.comparison <- table(df$fibroscan_steatosis, df.cut)
df.comparison df.cut
1 2 3 4 5 6 7 8 9 10 11
Cases 1068 924 29 154 0 28 1 4 0 0 1
Controls 2460 1318 31 83 1 5 1 5 4 2 0all plots (using cowplot)
combined_plot <- plot_grid(plot1, plot2, plot3, plot4, plot5, plot6, plot7, plot8, plot10, plot11, plot12, plot13, plot14,plot15)`geom_smooth()` using formula = 'y ~ x'Warning in as_grob.default(plot): Cannot convert object of class
tbl_dftbldata.frame into a grob.
Warning in as_grob.default(plot): Cannot convert object of class
tbl_dftbldata.frame into a grob.`geom_smooth()` using formula = 'y ~ x'
`geom_smooth()` using formula = 'y ~ x'Warning in as_grob.default(plot): Cannot convert object of class
tbl_dftbldata.frame into a grob.combined_plot
12 Interpretation of results
Using transient elastography, phenotypes were created for Steatosis (n=2209) and Cirrhosis (n =109). Multivariate logistic regressions revealed that body mass index (BMI) (OR=1.17, p <0.001), HbA1c (OR=1.37, p <0.001), triglyceride levels (OR =1.004, p <0.001) were associated with steatosis, whereas BMI (OR = 1.12, p<0.001), albumin (OR = 0.2299, P<0.0001), ALT (OR = 0.268, P= 0.029) were associated with cirrhosis. An 8:2 split of the data to training and testing sets yielded an AUC of 0.836 and 0.848 for steatosis and cirrhosis, respectively. Unsupervised machine learning using K-means clustering yielded 2 clusters with 60% (598/995) Steatosis + 2.9%(29/995) Cirrhosis in Cluster 1 and 31%(1611/5124) Steatosis + 1.5%(80/5124) in Cluster 2.
13 Conclusion
In summary, we realize that BMI is a strong predictor for the occurence of hepatic steatosis and cirrhosis. Other variables which are associated with each include alt, alb, gender (cirrhosis) and a1c, tg and alt (steatosis).
We have also successfully created supervised (using random forest) and unsupervised (k means clustering and hierarchihcal clustering) models to predict occurence of steatosis and cirrhosis.